If a time-traveller went back and killed their younger self, would that be murder or suicide?

Depends.

If time is a straight path and you only travel back along your own path to kill your younger self, then it's suicide.

However if you believe that time has multiple routes and that there may me multiple pasts and futures, then it would be murder. Killing your younger self in this manner might not be killing the you from your own timeline, but the you that took a different path. Therefore, technically, he's not you, because he chose a different life.

murder and I wouldn't want to do it. I would like to go back in time though and see my younger self and relive as I didn't know what I know now about myself, where I really came from. Only late in my life.

Suicide!

Neither - it would be impossible because if at some time in the past (younger self) he'd died (murder, suicide, natural death), he would be there in the future to go back to kill himself ..... I think that's right? lol

The pickle is, after killing their younger self, would they then disappear from reality

Its impossible. You would create a paradox. If you killed your younger self you wouldn't exist in the future to go back in time and kill yourself.

murder suicide?

Suicide is murder Both are wrong