you're filled with DETERMINATION

Speaking of Undertale: Weren't there like 4 save points in the rooms before Asgore?

didnt play it, but there were a few i think, as i wathed a letsplay

I feel if you save in a certain order you get a different ending.

I wouldn't think so; someone would have already found it in the game's code by now if that was the case. I think they're just there to make you think you're about to fight Asgore after each one, thus siking you out each time you save.