No, you will not receive any additional discount just because you rented a game for an extended period of time. Over time, the "Keep" price for a game may decrease, but there is no guarantee of that. You can choose to "Keep" a game at any time, provided that option is available for that title. The keep price will be listed next to the game in your GameQ.
No, there is no discount for that. The game prices drop right after they are new releases (on day one usually). 5% after you have been a member for 6 months. And 10 % after you have been a member for 12 months. You also get coupons to use as well. If you really want to keep a game, you also have the KEEP feature which is available as soon as the game is in (shipped) status on your AT HOME section in your Game Q.