It is allowed. Actually there is a file you can download where almost everything is unlocked. For those who just want to speedrun and not play the game or so =D

Actually endless has no specification like only/ any starter so you can do what you want =D And tbh I don´t think that it´s necessary for endless to have 2 categories. Just start with whatever you want.

And speedruns always starts from the selection screen. At least the record. Timer starts once you confirm new save slot/overwrite save slot

It wouldnt count at all. It doesnt mean "do 250 floors" or "do 500 floors". It means until floor 250 and until floor 500. So 1 - 250 / 1 - 500 / 1 - 750 etc