1.) You can purchase however much you want. It's all relative. DJ FC is rich and probably purchases trillions of coins at a time to invest a small percentage of his fortune. To you or I, that percentage equivalent may be half a bitcoin. The actual amount isn't relevant as long as you only buy an amount that you're okay with losing if things were to turn tits up. Not that I think things will turn tits up. But there are quite few people that heavily invested while btc was 1k+/coin that likely led to more traffic to suicide hotlines when mtgox went down.
2.) The site that you buy the coins from is an exchange that does allow you to have a wallet to also hold the coins. I suggest you move your coins out of that wallet into a more secure wallet.
The two items I mentioned above are more secure wallets where your data is secured on your local machine. This means that you could lose your wallet if your computer/hard drive takes a hard crash (but you can back the wallet up very easily into cloud storage or whatever else) or if your computer is compromised by malware or some shit like that (so don't let that happen). Basically, though, if you transfer your btc from the exchange wallet to either multibit or bitcoin core wallet (multibit is much faster, I'd suggest it), your wallet's integrity is in your own hands.
If you want to take things a step further, you can buy a
trezor. It's a hardware dealio that gives your btc wallet a physical presence meaning it's really only susceptible to "real-life" theft (not a great term, but you know what I mean).