Replace the word "robot" with "slave" in all of your questions and the answers become readily appearant. We had this discussion 200 years ago, then we fought as war and decided that all sentient beings have rights.

Keep in mind even the word "robot" is a word that literally translates to slave.

Proper term for what have right now is "automaton".

Once an entity is sentient or at least believes itself to be sentient then it has the same rights as all other sentient beings.

And before you drag out the whole "We built them we own them line".
We build our kids too,doesn't mean we own them, just that we're responsible for them.

Fact is though, ai won't achieve the level of sentience where it matters ever.
It's not plausible for a sentient mind in the human sense of the word to emerge from a system with completely different sensate pathways and totally different wiring.

More likely it will be a question of who owns our thoughts, when we are able to move our conscious state from one machine to another. That's more or less a matter of taking an existing conscious system and transfering it to a new substrate. We copy data all the time though and move entire VMs across multiple data centers while still running. I'm confident we'll figure that out for human minds as well.

Remember you are already a machine. Just an organic one running on chemistry.