Two questions:

1) How can I check my city's military unit's experience production (in terms of how much experience it produces per unit)?

2) Is there anyway to check (from a top down view) which city produces the most experienced military units (like the Coins Icon which appears in the city which produces the most economic output)?

1) build a unit
2) sorry i don't know what your about.

1) No
2) No
You have to figure it out yourself.

Not in the way you are thinking.

You can always go to the city screen and look at your improvements (ie barracks, HE) and great people (generals)