Would Thanos have Killed Hulk?

Yeah. The writers and directors have told us that Thanos is stronger than Hulk and doesn’t even need any Stones to beat him.

Yes, his intention was to kill Hulk which was why he got serious when fighting him but Heimdal got in the way before he could do any other damage.

No, I don't think he can overcome Hulk's healing factor.

According to the Rusos The Theory of Thanos refusing to Kill unless he had to was true. The seeing how easily Thanos beat down the Hulk I don’t Think Thanos would have saw him as a mission ruining obstacle the same way he saw Stark.

Yes.

If he wanted to, sure, no problems.

@lan_fan: MCU Hulk’s HF isn’t that good, if he even has one at all.

@green_tea: That joke scene in Ragnarok, where he jumped from the ship (lol), he healed very quickly.

Yes.

No, Hulk was clearly outmatched and defeated so Thanos would have no reason to waste time with him.

@anthp2000: Actually he was going to kill him one way or another but then he doesn't know that Heindall would have done that so he killed him......................

You literally answered your own question.

No. Thanos didn't want to kill anyone unless they got in the way of his plans.