I have been in US on a dependent visa while I received my H1B approval letter. Though I have new H1B approval notice, I have neither stamped/worked (no pay stubs) in my new H1B nor traveled in new H1B I-94. Can I transfer (change employer) my current H1B to a new petitioner from US in this case?
If yes, should I go to my home country for visa stamping or can I do a change of status from here?
Will there be any issue when I go to my home country and come back in the future?
In general you can go. In a worst case scenario, you might get a query with new processing that with out working why are you moving out of the current employer. you should be prepared with valid reasons.
Right now, I am in US on H4. So when I transfer my H1b, I will be applying from US with a change of status. Will that be an issue?
Also, can my current petitioner know in case my transfer with new petitioner ends up in RFE? Am I still eligible for working with my current petitioner?
As long as your previous employer not revoked your petition, you should be good. At a time you can have multiple H1b petitions in your hand. But only one employer can run your payroll.