Are there anything to care about in this universe?

yes you can care about 4 ''karmas'', with the last one being the intention to get enlightened, ie not getting any birth

And of what sort, brahmin is the deed that is neither dark nor bright, with a result that is neither dark nor bright, which, itself a deed, conduces to the waning of deeds?

In this case, brahmin the intention to abandon this dark deed with its dark result, the intention to abandon this bright deed with its bright result, the intention to abandon this deed both dark and bright with a its result both dark and bright, - this intention is called "the deed that is neither dark nor bright, with a result that is neither dark nor bright, which, itself a deed, conduces to the waning of deeds."

These four deeds I have myself comprehended, realized and made known."

https://obo.genaud.net/dhamma-vinaya/pts/an/04_fours/an04.232.wood.pts.htm#p1

A few comments on happiness...

“By stilling thought one kills Both good and evil deeds: Self-stilled, abiding in the Self, One wins unalterable happiness.”

Maitri Upanishad

“People often suppose that the realization of nirvana means the annihilation of all forms of existence. This is not true. What really transpires is that the illusions arising from our ignorance are extinguished, and we know true happiness, independent of any causes or conditions. And we continue to exist.”

The Dalai Lama - Reflections from the Journey of Life

“…[A]ccording to Aristotle, ‘it is necessary that there should be an eternal unchanging substance’ (Metaphysics 12, 6). This will impart change to other things, but will not itself change. Moreover, it will be immaterial, since it is beyond any sort of change or corruption. … It cannot itself change, because all change would be for the worse. And it contemplates the most perfect and best of things, and so exists in pure bliss or beatitude. What is the most perfect of things? Well, it is, so it must be thinking of itself. So God enjoys contemplating the divine being itself, knowing that it is the best thing there is. ‘Its thinking,’ says Aristotle ‘is a thinking on thinking.’ That is, it is the object of its own knowledge, and in such knowledge lies supreme happiness.”

Keith Ward - God: A Guide for the Perplexed

“It is possible to live in a state of stable happiness only when we are completely free of ignorance. Awakening puts an end to unconscious rebirth, and then the conditions and causes of painful effects disappear. This is the realization of a state of happiness which no longer depends on our external circumstances, nor on our emotions.”

The Dalai Lama - Reflections from the Journey of Life

You can enjoy looking at a lovely flower, even though you know it will die at some point. The colour and scent are not diminished by the fact it only lasts a few weeks/months.

I think Buddhism recommends you focus on what's virtuous and moral instead of on what's feels pleasurable.

For example, lying, killing, stealing -- are all to be avoided -- and that's important.

Conversely, generosity, kindness, keeping your promises -- that's important too.

There is a word -- sukha -- which might be translated "happiness". It's used in contexts like the Sukhavagga.

I suspect it's a happiness conditioned or caused by an absence not by a presence -- for example not happiness because you have something ("a chocolate bar") but happiness because of not having something ("anger", "greed", "remorse").

Are there anything to care about in this universe?

Yes, you should care about other sentient beings and practice putting their well-being foremost in your mind. If you have no experience with this, then try practicing the four immeasurables.

Due to impermanance of everything, Are there anything to be happy or sad about?

Rejoice in other's happiness! Rejoice when other's wishes come true! Rejoice in other's sorrowless bliss! Rejoice in other's progress on the path of dhamma as this is the hope of the world!

That happiness make sadness in the future (future includes next lives)

You've got it completely and totally wrong friend. How can happiness make sadness in this life or in the next? The problem is sentient beings don't know what happiness is or how to get it. We chase after things that do not lead to happiness thinking they will and we shun things that do lead to happiness thinking they won't. We are like a dog tied to a pole and wound round-and-round... we pull harder and harder to get free, but only succeed in binding ourselves tighter to the very thing that makes us miserable. We are quite silly and ignorant.

Are enlightened people happy?

Of course! They are immeasurably happy. Indescribably happy. Happy to such an extent that it is impossible to conceive. How do we know this? Because in order to become enlightened they must work for countless lifetimes at accumulating and working at the causes of happiness! They must perfect all virtuous conduct! They must perfect all virtuous minds! Take them to their zenith! Imagine a mind as wide and deep as the ocean filled with the most altruistic and peaceful thoughts. With absolutely zero ill-will and focused on other's well-being to the limit. Such a mind... we cannot even begin to describe the happiness it entails!!

Or neither happy nor sad?

You need to work on discovering what happiness is and the causes and conditions of happiness. Fortunately, that is exactly what the dhamma teaches. Your confusion is caused by misunderstanding. Rest assured you have it blinkered, but keep working at it and working at it and working at it... don't stop! and you'll slowly unwind that leash holding you to the pole.

Dhamma is the Ultimate Medicine. Buddha is the Ultimate Doctor. The Sangha are the Ultimate Nurses.

The disease is dhukka and unhappiness. The cure is happiness... immeasurably so!

OP: Due to impermanance of everything, Are there anything to be happy or sad about ? Even about dhamma ?

Are enlightened people happy ? Or neither happy nor sad ?

From AN 9.34 (translated by Bhikkhu Sujato):

Ven: Sariputta: “Reverends, extinguishment (Nibbana) is bliss!
“sukhamidaṃ, āvuso, nibbānaṃ.

Ven. Udayi: “But Reverend Sāriputta, what’s blissful about it, since nothing is felt?”
“kiṃ panettha, āvuso sāriputta, sukhaṃ yadettha natthi vedayitan”ti?

Ven. Sariputta: “The fact that nothing is felt is precisely what’s blissful about it.
“Etadeva khvettha, āvuso, sukhaṃ yadettha natthi vedayitaṃ.

Sukha or happiness for an unenlightened person is experienced when encountering pleasant feelings (from the six senses, including thoughts and the intellect) or when encountering the cessation of painful feelings (from the six senses). But for an arahat, sukha or bliss (in this context) is experienced when encountering neutral feelings, no feelings and Nibbana.

Please see this answer for commentaries by Nyanaponika Thera. The supporting suttas are MN 44, SN 36.5 and AN 9.34.