Hi, please explain to me the basics of a good opening fundamentals

Pure basics are:
1. Pawn in the center
2. Develop your pieces
3. Get your king safe (this doesn't necessarily mean casting!)
4. Connect your rooks
(5. Rooks on open files)

Combine that with some tactical knowledge and you're fine.

I would mainly study openings to know a few concrete things (tricks and traps) and general ideas. It's not very necessary to memorize specific moves and variations too much.

What about the pros and cons about indirect controls (fiancheeto) compared to direct pawn-to-pawn contest at the center?

All moves related to the centre are good. It does not matter if it is occupation of the centre or control of the centre.