UK Family Permit Application and Supporting Documents

I would like to know the list of documents I should provide...

Since you are recently married, you will probably be suspected of a "marriage of convenience," but evidence that you live together should overcome that, so do include something showing that you live together.

Other than that, all you need is your passports and your marriage certificate. If the certificate is not in English (or Welsh!), it should be accompanied by a certified translation (as should your evidence of cohabitation).

...and whether my wife should accompany me to the interview (submitting the documents and biometric data collection) or not.

It is not necessary for your wife to accompany you.

How should we prove that she's traveling with me? should I provide flight tickets? or would a cover letter from her addressed to the UK authorities attached with the other documents suffice? and how would such a letter be written and sighned\certified?

I once prepared an EEA family permit application for my mother in law, who was planning to use it for a short visit. I do not remember whether we submitted copies of the flight reservations, but I suspect we did not, because I doubt we would have made the reservation before the permit had been approved. A simple statement that you plan to travel together should suffice. There's no need to have it certified.

I got the family permit by mail earlier today.

I did not get an email saying I'll get it today though. I just got a phone call from aramex.

I sent with the application, the marriage certificate, a lease agreement showing my and my wife's names, screenshots of past conversations, my wife's tarjeta sanitaria and her passport. (All copies) no idea why they didn't accept the originals, maybe it's different for other people though so take your originals please.

Your question is mixed, one place you are asking for family permit and also mentioning that you need to visit UK. A permit is only issued when you are allowed to work, study or you are here for business purposes and that is referred as British Resident Permit or BRP.

If you are applying from Palestine, I doubt you might have an embassy there, just make sure what documents you submit should be in English, if they are translated in any other language they need to be translated into english and certified as true copies of the original.

And asking about your income is not an un-necessary question, all countries ask this, that is the sole purpose upon which they grant you visa entry into any country, they don't want someone to end up permanently in their country. So you have to clearly mention your source of income, whatever that is.

Always refer to www.gov.uk website for complete lists of documents that need to be submitted along with the application.