Sounds like a bad idea in general. Any data use agreements get lost, shadow-IT brews and nobody knows what tools to use, oh and it's against the service terms.
Generally not, since the corporate account has all the privacy knobs turned up. I use my personal account on my open source projects, where code leaks aren’t exactly an issue.
Unless you get written permission you can be sued for publishing their trade secrets. This can end in jail time if your employer is particularly uncaring.
I pitched this to management as a way to get a very expensive fine tuning job done for free. They're not quite across that line yet but we're getting closer every day.