You can do almost anything in English. I think I've only needed to speak Estonian to talk to old ladies in shoe repairing shops and the like.
Quite. Worth it, if you're staying for the long term, but pretty hard.
Do you have a degree in computer science or quite a bit of IT experience? If so, you're relatively likely to find some sort of job even with English only, as far as I've seen. Otherwise, it'd be quite tricky.