Are there any benefits to owning the strip? If I kill Mr. House can I be in good standing with the Legion? If I own the strip, will the perks be obvious? Or will I just have access to the Lucky casino and everything stays the same?

If I don't go with the Yes Man quests, do I have to hand the platinum chip to someone?

Sorry about all the questions, thanks if you answer any of them.

You can't really own the Strip unless you do the Yes Man ending. And then the game ends.

If you kill House, that just means you killed House, it doesn't automatically pass the Strip onto you. So things will stay the same for you, and it won't hinder any questlines, other than House's.