I'm nearing my end of of Persona 3, and I really want what FES has to offer. I plan on selling my copy of P3 for FES. So,  if I buy FES, will it read my P3 memory and I can resume my journey?

yeah pretty sure

Yeah, but keep in mind that all of your equipment will only be useful inside 'The Journey', the main Persona 3 story. 'The Answer', the extra chapter that FES has, has you starting from scratch and none of your items etc. carry over. I found it kinda interesting on the story front, but 'The Answer' wasn't that great to be fair. It removes a lot of the gameplay, pretty much focusing exclusively on battles and grinding. Not too fun.

If you transfer your data from P3 to FES, you will have to start the game over from scratch, and from memory, its like a new game+ with only the academics, charm, courage, persona compendium and max s-link items carrying over.

There's only one new social Link (Aigis) which doesn't start until the final month. There is also one new school event and some new scenes like the koromaru walks, control room videos, and Elizabeth dates, plus some new personas. If you want to see all of the new stuff you'd have to start over any ways, and the changes aren't really going to make the game seem new or anything-they're just nice bonuses.

The Answer is a nice epilouge story, but if you hate grinding it will be a chore. Personally I'm liking it so far-the story is interesting, you just don't get much of it.