Mixers are a good way to keep anonymity. That's why they still exist ^^
Not really.They don't make the transactions disappear.If I'am not wrong,a few tools are available to trace the origin address of an transaction.
Of course there is nothing that leaves 0 traces.
For example, justice could impose to mixers to reveal their loggs.
They don't do that.However,they can if they want to.I mean obviously if Legal Authorities are involved.]
That's a bit like a VPN, it's not a total annonimity, but it helps a lot! Unless you sell drugs of course :3
Why else do you think wanna use mixers ?