Reported speech

1) He wondered when would Tom published his story.
2) Someone asked me to know where was she studing?

Someone asked me if I knew where she was studying. / Someone asked me to find out where she was studying. No question mark -?- 

3) We asked she where did she go if she would have a free time.

We asked where did she go when she had free time.

We asked where would she go if she had free time. 
4) She asked what they had done since they finished the university :)

Good English. Meaning very clear, and would not be a problem when speaking. Hopefully these small corrections make it more clear.