I have a few questions, I figure r/ gaming would be able to help me out more than any other subreddit - details inside

So for the last 3-4 years I haven't played many games at all. At all. This has been due to a number of factors (college, lack of time, other things, having a shitty PC). I live in Australia, but am visiting the US for a while -

I decided to get Steam, very easy and convenient system. It's excellent. TF2 was super fun. So I have a few questions -

1.) If I decide to purchase many many games while I'm here in the states (since they are considerably cheaper than the .au prices) will I still be able to download them and play when I get back to Australia ?

2.) What are the best games under $10 that will run smoothly on a mid range laptop. (It's a HP pavillion notebook).

3.) What games should I purchase (after I get a decent gaming rig ?). As in what are the games I've missed out on over the past 3 years that I absolutely must play ? Money isn't really an issue. Thanks !