1) "Immediately" - "I'll come at once".
2) "Simultaneously" in the sense of someone doing two things or being at two places simultaneously. "I can't be in two places at once." "I can't do two things at once." There's usually a tone of defensiveness or frustration in your voice because someone's asking you to do too much:
Little Johnnie: Will you help me with my homework, mummy?
Mummy: I'm getting the dinner on and I can't do two things at once.
"At once" is not used when you want two say that two things happen simultaneously. You'd say "The two bombs exploded simultaneously" or "...at the same time."
But you can say "Everything happened (all) at once." There's an idea of suddenness or perhaps even confusion.