These are shortened replies and seem to take advantage of the fact that perfect and continuous tenses are formed using past and present participles. So a bare participle phrase can be understood as standing in for the corresponding tense. This is especially natural when the helping verb would be reduced to a clitic and attached to the subject
So you can have the dialogue:
What have you done recently
(I've) hung out with my friends.
What are you doing tomorrow?
(I'm) hanging out with my friends.
This is not really possible with a simple tense.
What did you do yesterday?
I went to the movies.
You can't remove the subject here because you get an incomplete sentence, and not a complete participle phrase. It might be possible to say "went to the movies" when writing in "telegraphese" but it isn't natural in speech. To me if you said "went to the movies" it sounds like a grumpy teenager talking to their mum and trying to avoid contact.
It would be okay to reduce to a complete noun phrase
Where did you go yesterday?
In all these examples the reduced form is not "correct" if you are speaking carefully and in complete sentences. All the shortened examples are possible in casual conversation. It would often be better and more natural to put the subject and verb. Normally the person replying would want to give some more details, rather than minimise the number of words. Conversation is a dance for two, not yoga.
What have you done recently?
Oh, lots of stuff. I've hung out with my friends a lot. We went bowling last Saturday, which was fun.
Yeah. Do you know Martha?
She got 129!