1. I met her in mid July.

Question

2. I met her in middle July.
3. I met her in late July.
(Are all grammatical? Which one is correct #1 or #2?)

Answer 1

#1 and #3 are correct. To use "middle" in #2 add words to make it "I met her in the middle of July," which is more correct.

Answer 2

Thank you.

In the middle of July
at the middle of July

(Do we have to use 'in'? What about 'at'?)

Answer 3

In the middle of July is better. For information, common usage is to hyphenate mid-July. At indicates a precise point, and it is not used much. You can use it...

At the middle of May, school is out.

but the more common usage is "in".