It might be out of gas, the token is locked, or anything else. It would be better if you will check etherscan for every transaction you made to see the reason why it was failed.

What do mean exactly with these two?

Myetherwallet is just an interface, a platform. In terms of security, the individual is responsible for that. We know that MEW aren't holding the private keys plus there's no accounts (username/passwords) in the site. That being said, implementing 2FA is impossible.