4 - There are many reliable exchanges out there. For starters, again, Bitcoin is super anonymous. None, that I am aware of, require any personal information. Obviously, Blockchain is completely secure and just using Bitcoin requires no information. If you want to use an online wallet, you can use Xapo or maybe Coinbase - both are secure and don't require info to send and receive. They do require info to deposit but that's obvious because you need a CC or bank account to deposit. An exchange to sell Bitcoin for altcoins is Poloniex. This is my favourite and requires only an email, password and BTC address.
Coinbase has been known to ask for ridiculous amounts of ID, even video identification at times, and can suspend your account if they associate you with activities like gambling. If you hold all of your Bitcoin on an online wallet, you don't own Bitcoin because they have your Bitcoin and just promise to allow you to use it (they use it on your behalf), so if Coinbase was ever unable to pay it would stop working. Blockchain.info is more secure but still not ideal. You should be using desktop wallets if you really value your security or privacy.
That's true and I do not recommend using Coinbase at all. I should rephrase my post by saying those are some examples of exchanges but I do not recommend using Coinbase. However, to clarify, when you first begin using Coinbase you're allowed to send and receive Bitcoin transactions without any problems. I stopped using the service years ago because I've heard of all the cases of stolen BTC, but my account is still totally private. The most info I ever gave was my phone number -- and that was voluntarily.
You're right though when you say that they will suspend your account for "gambling" or other reasons. The reality is that the safest Bitcoin wallet is none at all. So, if you want to be a little safer, just try the desktop version. But I'd recommend to OP that he spreads his BTC to all sorts of different locations on a variety of different platforms. Diversification can really save you some cash.