First off, a couple corrections:
He sees a fly on his leg
See is the third-person plural form where sees is the third-person singular form.
He saw a lady in the crosswalk
The preposition in is more idiomatic here.
The way sentence #1 is structured strongly suggests that "on his leg" modifies "fly". To make "on his leg" modify "sees", restructure the sentence like this, using a parenthetical phrase:
He, on his leg, sees a fly
However, this is uncommon and unnatural phrasing. It's not even entirely clear just from the sentence itself how exactly "on his leg" modifies "sees".
Addressing questions #2 and #3, it seems that you've got the meaning of the articles slightly confused. The indefinite article "a" refers to some general, unspecified lady. The definite article "the" refers to one specific lady. Both articles are used with "lady" which is singular. The difference is referring to a specific noun or not.
Did he see anyone in the crosswalk? He saw a lady in the crosswalk.
Where is the lady? He saw the lady in the crosswalk.