I was wondering if I join PS Plus in the US, will I be able to play downloaded games when I'm in another country? also, will I be able to purchase game or renew PS plus in another country? Thanks
The short answer is yes to all your questions.
If you paid for the game you can play it indefinitely regardless of location or internet connection.
If you got the game for free via PS Plus you can play it as long as your subscription for PS plus lasts, regardless of internet connect and location. You will need to go online to renew you subscription however you can do this overseas for your US account.
You can make purchases and download content from your US PSN account from any location with an internet connection but you will be restricted to the US playstation store. You will not be able to access content on the local store without creating a new local account on a new PS vita card.
Source: I currently access and make purchases from the UK PSN store on both PS3 and Vita from Australia no problem, I even bought both units in Australia.