How exactly are sectors and systems found?

Also, is there a way to buy them from the factions that control them? If not, do you think there should be?

You can buy them IF they will sale them, which they do not. And to find a hidden system you have to search for them. One DS coord at a time, it is long, boring and mostly unrewarding experience.

Sectors aren't 'found' - they exist. There are no hidden sectors - what you see is what there is.

As for hidden system, as Xakic says you just mindlessly trawl empty sectors hoping that they put a system in that area, and that you find it. Mindnumbing work, but with a good payout at the end if you succeed.

As for buying planets/systems sure - its been done many many times in the past. But expect to need billions in assets and rare tech etc before you can really think of owning a planet. An asteroid or possibly a moon, maybe, which are 'merely' in the hundreds of millions in cost.