"What do I dislike doing?", why not?
Why it can't be " what i do not like"
What do I not like would be "що я не люблю"... The verb 'робити' means "to do"... So "що я не люблю робити" would translate to "what do I not like to do" (hope this helps)
Why does the 'я' sound unstressed and more like a 'є' sound ?
By stressing "я" you slightly change the meaning of the question. It sounds like you are not sure if the question is about your likings or someone else's and you are clarifying it.
The unstressed "я" does not sound like "є" to me.
I do not have access to a Ukrainian alphabet