1. Playing as the runner and having all memory slots occupied, can I 'overwrite' some programs to install another ?

2. Again, as the runner, having scored 'Priority requisition' can I rez 1 ICE of corp ?

1. Yes. You can do this even if you aren't at your memory limit.

2. No, agendas are only active in the corporation score area.

"The Runner can choose to trash any number of his installed

programs at the beginning of an install program action." Core Set Rules p.15

While nungunz did say a true fact (and a very important one that will save you many a future question post), it's not actually the reason that the answer is "no." It's a little more subtle and not immediately obvious from reading the rulebook. Runners "steal" agendas, corps "score" agendas. So the text on PriReq (and many other agendas that the runner would love to take advantage of) isn't actually triggered. You'll notice that for quite a lot of game terms there are different nouns and verbs used for each side of the table. This leads to pretty granular criteria for various effects. Check out the "Film Critic" card and think about how it would interact with cards like Casting Call, Fetal AI, or Punitive Counterstrike.

Wow, that really opened my eyes. Looks like you've got to be careful at every step and point of the game. Thank you for that explanation. Really appreciate it.

It's also true that Agenda text isn't active in the Runner score area.

Rulebook p.14

While an agenda is in the Corporation's score area, it is active and adds its agenda points to his score.

(emphasis added)

Compared to p.18

While an agenda is in the Runner’s score area, it adds its agenda points to his score.

So nungunz was perfectly correct in his statement. While not relevant to Priority Requisition (which has an effect when scored) it does matter for cards like Government Contract.

Also, in the case an agenda can be used from the runner's score area (see: 15 Minutes), the card will explicitly say so.