Hi Robert, I wellcome you to the bitcoin community. You will soon find it fun to be part of this movement crzy things happen but it's all part of the game. No one can say if it's safe to use any of the brokers, given some human and hacking issues in the last month have affected their credibility but most people still use them (this is not the only way to exchange BTC, there are losts of bitcoins sold OverTheCounter, you can find links at bitcoin.org). I think that most people using this online exchanges worry less about if they are sending money to someone that will run away (which i guess is your concern), it dosen't seems so, but worry more about if they are running their bussiness in serious and safley way as for not loosing all the coins from one day to another.
The coins are generaly saved in their online wallets which then can be send to your personal wallet.dat in your PC at will. Perhaps some send them directly to your PC, I don't know.
About the third one, If your transactions will be buying with offline cash, yes, but you could always send BTC form one wallet to another to sell BTC in one or another broker.
Good luck, come on in and have fun.