"Solipsism is the belief that there is only one mind, and all other people are philosophical zombies, right?"

Not exactly. Solipsism says the only thing a mind can know for sure is its own self-existence. The corollary is that the existence of other minds can never truly be known. That it can never be known if others are just philosophical zombies.

This is different from "believing there is only one mind." That would entail the affirmative statements:

1. It can be known whether or not others are philosophical zombies.
2. Others are in fact philosophical zombies.

Solipsism does not hold these two affirmative statements.

"Buddhism Every Buddhist believes that only he has consciousness, and all other people are philosophical zombies?"

No, this is just wrong.

"Hinduism Every Hindus believes that only he has consciousness, and all other people are just philosophical zombies?"

No, this is just wrong.

In summary, none of the three - Solipsism, Buddhism, Hinduism - believe those two affirmative statements.

Solipsism is not a religion or philosophy. It's just a speculative idea: "hmm how do we know the world we experience actually exists? What if our senses and minds are fooling us and nothing else exists at all?". I don't think there are many people, if any, who seriously believe in solipsism and make it one's guiding principle. It's just a philosophical joke people are playing with as they study philosophy.

Note how Solipsism doesn't say "other minds don't exist", no, - instead it says "I definitely exist because I can think and experience stuff, but there's no proof that the rest of the world exists other than in my mind".

Hinduism is not a concrete thing. It's a huge collection of traditions, myths, rituals, and teachings that developed over millennia in many different places on Indian subcontinent. There's no single system there. But in context of your question we can say that most people who roughly belong to this group, called Hindus, believe that people have souls and these souls are parts of the Universal Soul (call it God or Brahma or whatever). Some of the people in this group also believe that this Universal Soul is sleeping and this world is a dream this Universal Soul is dreaming up. Again this idea of the world being God's dream is more like a metaphor or beautiful myth, I don't think all Hindu people take it literally (although some might).

There's no teaching in Hinduism that says that other minds don't exist or the world doesn't exist at all. They usually say this world of separation is an illusion or like a dream, and when the soul wakes up it realizes its unity with God or Brahman, and sees everything correctly as it really is. Note how they don't say nothing else exists, they say the awakened soul sees the true reality, and in this true reality everything is God, basically.

So in solipsism you are the only reality and everything else is illusion while in Hinduism all separate things are illusion and the unity of Everything with God is the true reality.

Now, Buddhism is not a single thing either. It's a huge collection of ideas and teachings that developed from one person's teachings. People were trying to implement this teaching, interpret it, and understand its implications - and this original teaching along with its historical interpretations and implications is what we now call Buddhism.

Many Buddhists (although not all!) will say that soul does not exist, this makes them very different from Hindus who strongly believe in soul. (There are some Buddhist whose faith is more like a hybrid between Buddhism and Hinduism but we can omit them for simplicity). Moreover, most Buddhists do not believe in Universal God or Universal Soul, whatever you call it. In this sense, Buddhists are more like the modern scientific materialists - they think the world works according to some kind of natural laws. Not necessarily same exact laws we know from science but laws nevertheless, not a God dreaming things up.

Now when it comes to mind, most Buddhists will say that mind also works according to some laws, it develops and changes based on causes and conditions - not randomly. When this mind develops, it comes up with all kinds of ideas about the world, including the idea of "I" or "self" - but according to Buddhism all these are just ideas, just concepts the mind develops to approximately understand and analyze its experiences.

So in Buddhism we don't say other minds don't exist or the world doesn't exist, no. We say, the reality or the world we experience is an interpretation we make based on our experience, prejudices, on where we focus our attention and on our emotional state.

In Buddhism we often say that this world is like an illusion or our life is like an illusion, meaning that it seems to look a certain way until you look closely. This doesn't mean the world doesn't exist, it just means when our minds are childish our world is primitive, and as our minds mature - our world becomes much more deep, nuanced, more complex, and a more accurate representation of how-things-really-are.

As you can see, Solipsism, Hinduism, and Buddhism are three very different things. None of them says that other minds do not exist. Only Solipsism says the world outside our mind may not exist. Hinduism and Buddhism both say our experience of the world is not accurate. Hinduism says, in reality everything is one with God, while Buddhism says that every experience of a certain subjective world is a result of causes and conditions.

Solipsism is just a toy philosophy, it's not meant to be a real belief.

Hinduism teaches (among other things) how to strive for unity with God, both in this life and beyond.

In Buddhism we learn how our lives are shaped by causes and conditions, we learn how we create these causes by our actions, we learn how mind works, we learn how it develops illusions and superficial ideas about the world, we learn how these superficial ideas keep us entrapped in certain subjective realities, going in vicious cycles - and we learn how to liberate from all that.

By the way, Buddhists come in many ethnicities like Thai, Burmese, Sri Lankan, Cambodian, Vietnamese, Chinese, Japanese and even English persons like Ajahn Brahm or Germans like Bhikkhu Analayo.

There are different schools and sub-schools within Hinduism and also different schools and sub-schools within Buddhism. So, for this answer, I will limit the scope. I choose to limit it to Advaita Vedanta in Hinduism as taught by Adi Shankaracharya in his own writings, and teachings from the Early Buddhist Texts (EBTs) in Buddhism, especially the Pali Canon.

Solipsism in western philosophy

From wikipedia article on Solipsism:

Solipsism ... is the philosophical idea that only one's mind is sure to exist. As an epistemological position, solipsism holds that knowledge of anything outside one's own mind is unsure; the external world and other minds cannot be known and might not exist outside the mind.

Solipsism doesn't say other minds don't exist. They say, "we're unsure if other minds exist". Solipsism states that we're only sure of our minds and unsure of everything external to it.

Hinduism (Advaita Vedanta)

Brahman is God, Atman is Self, jiva is individual self.

From Adi Shankaracharya's Vivekachudamani:

234. If the universe be true, let it then be perceived in the state of deep sleep also. As it is not at all perceived, it must be unreal and false, like dreams.

251. All modifications of clay, such as the jar, which are always accepted by the mind as real, are (in reality) nothing but clay. Similarly, this entire universe which is produced from the real Brahman (God), is Brahman Itself and nothing but That. Because there is nothing else whatever but Brahman, and That is the only self-existent Reality, our very Self, therefore art thou that serene, pure, Supreme Brahman, the One without a second.

252. As the place, time, objects, knower, etc., called up in dream are all unreal, so is also the world experienced here in the waking state, for it is all an effect of one's own ignorance. Because this body, the organs, the Pranas, egoism, etc., are also thus unreal, therefore art thou that serene, pure, supreme Brahman, the One without a second.

From Adi Shankaracharya's Aparokshanubhuti:

56. This world, though an object of our daily experience and serving all practical purposes, is, like the dream world, of the nature of non-existence, inasmuch as it is contradicted the next moment.

57. The dream (experience) is unreal in waking, whereas the waking (experience) is absent in dream. Both, however, are non-existent in deep sleep which, again, is not experienced in either.

58. Thus all the three states are unreal inasmuch as they are the creation of the three Gunas; but their witness (the reality behind them) is, beyond all Gunas, eternal, one, and is Consciousness itself.

59. Just as (after the illusion has gone) one is no more deluded to see a jar in earth or silver in the nacre, so does one no more see Jiva in Brahman when the latter is realized (as one's own self).

So, according to the quoted verses, we see that the world that is perceived in a dream is unreal, after waking up. Similarly the world that you observe when you're awake does not exist in the dream or in deep sleep (turiya).

However, what is common in all three states, is Consciousness, the silent observer. And this Consciousness is Atman (the Self), which is the same as Brahman (the Ultimate Reality). This is a gist of Advaita to my understanding.

So, Advaita is very centered on Consciousness, the silent observer.

Although there are many living beings, there's only one Consciousness = Atman (Self) = Brahman. The perceived diversity of living beings and inanimate objects is a mirage or a dream or an illusion when Consciousness looks through the lens of maya, similar to living beings and inanimate objects perceived in a dream.

So, it is very clear that the universe is unreal and is an illusion in Advaita. The awake, dream and deep sleep states are all unreal (see Aparokshanubhuti 58). The only thing real, eternal and permanent is Consciousness = Atman = Brahman.

The enlightened person sees only Brahman, while the unenlightened person suffers because of the illusion of separation from Brahman and of diversity in forms.

Buddhism (Pali Canon)

The Buddha's teachings from the Pali Canon is quite different. It does not use the word "maya" but it does have the concept of illusion or mirage.

By convention, a sentient being in Buddhism is one where the five aggregates of form, feeling, perception, consciousness and mental formations come together, just as when different parts of a chariot come together, you call it a chariot (SN 5.10).

Through dependent origination (pratityasamutpada), the mental idea of the self (atman) arises. Just as how different parts of a lute (vina) interact to create music, the five aggregates work together according to dependent origination to create the mental idea of the self. If you break down the five aggregates into their constituent parts, you will not be able to find the self anywhere, just as when you break the lute down, you cannot find music anywhere (SN 35.205).

Consciousness in Buddhism is not independent. It is dependent on the six sense media of eyes, ears, nose, tongue, body and mind or intellect (for thoughts). So, dependent on this, there is eye-consciousness, ear-consciousness, mind-consciousness etc. (MN 38)

The mind not just objectifies the mental idea of the self, but it also objectifies and classifies all that is perceived into non-self objects, relative to the mental idea of the self or based on its relationship to the mental idea of the self. This is also called reification or concept proliferation (papañca in Pali or prapañca in Sanskrit) (MN 18).

For e.g. a cooked meat dish is perceived by a meat lover as delicious food, by the vegan as something repulsive, and by the honey bee as dirt (because it is not its food). In this sense, the "delicious food" or "repulsive thing" doesn't exist, except as objectified and classified by the mind.

Another example is the sea. A fisherman looks at the sea as a source of fortune (like how a miner looks at a gold mine). A sailor looks at the sea as a place of adventure. A person who doesn't know how to swim and rarely spends time near large bodies of water looks at the sea as a dangerous place. Meanwhile, a fish may not perceive the sea as a body of liquid at all, since it is all around it. In this sense, the sea as a "source of fortune" or "source of adventure" or even "body of liquid" doesn't exist, except as objectified and classified by the mind.

So, in Buddhism, the universe itself is not a dream or a mirage or an illusion. But rather, how the mind objectifies and classifies what it perceives is what is unreal. Also, dreams are just thoughts in the mind based on what has been perceived before, observed by mind-consciousness.

An enlightened person will see things exactly as they are (MN 1). Meanwhile, reification (papañca) is a source of suffering for the unenlightened person, because craving is a habit of reification (this question, MN 1, Snp 4.14), and craving (taṇhā or tṛ́ṣṇā) is the cause of suffering (dukkha) in Buddhism i.e. the second noble truth.

Through enlightenment, ignorance is uprooted, eliminating self-view and reification. This in turn will eliminate craving, which eliminates suffering.

Summary

Solipsism states that we're only sure of our minds and unsure of everything external to it.

In Hinduism (Advaita), according to Adi Shankaracharya, the universe is unreal and an illusion. Only Consciousness = Atman (Self) = Brahman (God) is real. The illusion appears so when Consciousness looks through the lens of maya (illusion). There is only one Consciousness (God), while the multiplicity of minds is simply an illusion.

Meanwhile in Buddhism according to the Pali Canon, which is an Early Buddhist Text (EBT), the universe itself is not explicitly considered unreal or an illusion. Rather, that which is reified in the mind is what is unreal and an illusion, and a cause of suffering. There may be other minds of course.