I would only use Coinbase to initially buy Bitcoins. Then if you want to do trading frequently between fiat and Bitcoin, use an exchange like Poloniex or one of the other good ones by transferring from Coinbase to that exchange. Then if you want to cash out permanently, transfer back to Coinbase.
Do not use Coinbase. The US government wants to get all their customer's information and transaction records. I will not risk using them and have my name recorded in their database. Coinbase has declared that they will fight the case but that will cost them a lot. I believe they will give out all their records sooner or later.
Yes. I would strongly suggest using a desktop o local Wallet than Coinbase.
Localbitcoins may have a high value than coinbase but it is better than that in many ways. For EU people kraken is good compared to localbitcoin.
