Are you referring to blockchain.info?
If so, no, they can't.
They can easily feed you malicious javascript when you are logging in so your password goes to them instead of decrypting it in your browser.
So, yes, they could.
In that case, any wallet provider can do that, including Bitcoin Core.
Yes. However there is an additional question.
Can they get away with it with nobody being able to prove they did it and have 1000 users even proving that they did not do it?
And is it possible that only one possibly some shop floor level server operator can do the stealing with nobody else even some higher up from the company knowing about the theft and who did it.
For an online wallet the answer is yes, trivially.
All they need to do is for one time feed the malicious javascript to one user only which they have selected to be the one they want to steal from. The probability that everybody inspects their javascript EVERY TIME they use the online wallet is just ridiculous.
Clean up the server and nobody knows what happened with no proof available to anybody and blame a keylogger in the victims computer.
Have 1000 users inspecting THEIR javascript to "prove" that the javacsript from the company is safe with no backdoors.
Has that happened already? You betcha.
For bitcoin core the answer is no.
The proof about the malicious code remains out there forever and traces about who put it in there.