I shedded so many tears for them.
This is correct. "I shedded" is a more lyrical or emotive way of expressing "I have shedded".
Is there any place to eat around here?
Is there any place to get something to eat around here?
Correct, though it is more common/colloquial to say 'anyplace' or 'anywhere' instead of 'any place'.
Let me know when you're getting off. (a bus etc.)
Correct. An alternate form that is probably more common is, "Let me know when you get off".
I'm paying you to do what I tell you to do
I see her wherever I go / I see her everywhere I go.
Correct. I would favour the 2nd, but the first is fine.