Is detachment all about not giving damn to peoples/things?

In Buddhism, detachment always comes with compassion. For an outsider it sounds rather strange because these two sounds rather incompatible. Any outsider usually would equate detachment with aloofness. But the type of detachment that a disciple of the Buddha develops helps to see the truth more clearly. It also helps in being more impartial when judging.

Being detached helps to keep that little voice in you at a distance – the inner voice that tends to mislead you from the true path. It holds this little voice at bay. Then when meditating with detachment, keeping a certain amount of distance from the activities of the mind helps get some perspective on what comes to mind. So this kind of detachment is not at all about not giving a damn to people or things, but the very opposite of it. In practicing the teaching of the Buddha, it is important to develop a sense of detachment. Mindfulness is the most important factor that helps in this.

Sorry I don't have much spare time so I'm going to write this answer mostly using hyperlinks.

I haven't heard the phrase "Everything is lust and mirage" before (is it a quote?), but it sounds like it's talking about the main two of the Three Poisons.

Also "not giving a damn" (in the title) sounds to me like the third poison, i.e. "aversion" or "hatred".

There's something (a concept) called 'attachment' in Buddhism, which is sometimes also translated into English as 'clinging' or 'grasping'.

The Sanskrit and Pali word is Upādāna, and (according to Wikipedia) the Tibetan is len.pa (lenpa).

Wikipedia articles about it include:

• Upādāna
• Attachment as one of the Twelve Nidanas.

There's a concept called 'attachment' in Western psychology: Attachment theory

Although that's the same word (i.e. "attachment") in English, it's not exactly the same theory!

Similarly Western psychology uses the word 'detachment' in various ways, see for example Emotional detachment.

Again this (Western meaning of ) "detachment" isn't exactly the same as what Buddhist theory recommends. To avoid that automatic association between Buddhist and Western meanings, caused by using the same word ("detachment") for both, it might be better to use a slightly different word, e.g. "non-attachment" rather than "detachment".

And in fact I'm not sure that Buddhists do talk about detachment or non-attachment very much. Instead perhaps they warn against the dangers of "attachment": and recommend as an antidote, not "detachment", but rather maybe "renunciation" or "equanimity".

Related to non-attachment is the Buddhist term Nekkamma (renunciation). The original version of the question included the monk tag, and indeed it's maybe "renunciation" for which Buddhist monks are famous. Suttas in the Pali canon recommend renunciation.

I think that Buddhist lay people don't (and probably cannot) practice renunciation in quite the same way as Buddhist monks.

I note without comment that Nekkhamma is listed among the 10 perfections of Theravāda Buddhism, but isn't in the (shorter) list of 6 perfections of Mahāyāna Buddhism.

Buddhist theory recommends attitudes called Four Brahmavihāras. These include Compassion and so on, which (to answer your question) is not the same as "not giving a damn".

One of the brahmavihāras is Equanimity. Note that "Indifference" is described as a near enemy of equanimity which means that indifference might seem similar to, but is actually an opposite of, equanimity).

Life has no requirements, including loving and caring. This is social programming talking.

Life just is.

Furthermore, in Buddhism life is originated from ignorant perception ( see 12 nidanas) so on top of just this is-ness... Buddhism recommends that we fix our ignorance--which requires us to go about the Buddhist self-training process towards a natural happiness and freedom.

Lastly, detachment is NOT indifference. It is about not attaching.

This is why it is usually better to translate detachment as "non-attachment" meaning there is no fabricated attachment.

If attachment happens, you don't attach to getting rid of it. (i.e. forcing away your crush on someone)

If attachment doesn't happen, you don't attach to forcing it. (i.e. forcing yourself to like your biology studies.)

If attachment has already happened, you don't attach to making more of it or making less of it (don't add energy to an obsession with something if it has arisen in your mind, but don't repluse against it if it is continuing at the moment).

Just get Right View (the first step of the Eightfold Path) and non-attachment will arise naturally.

Follow the rest of the Path accordingly including Right Effort and Right Action and Right Livelihood.

Study the Four Noble Truths more in-depth and you will be really grateful that there is such a balanced, perfect, practical system to self-perfection for all-time.