A NON-TEACHER'S OPINION
(1) May I start the discussion?
(2) As you said, "what" in your sentence is a relative pronoun.
(3) My books tell me that it is usually interpreted as:
that which / the thing that
(4) I do not know whether it can be interpreted as "doing something that."
(5) I shall wait along with you for someone else to answer both this question and
your second question, which I also find very interesting.
Have a nice day!
Interested in Language