Its fine. Seeing as its a window ac unit there likely isn’t anywhere else to put it and its not like they’re going to have both running at once and the baseboards don’t often have a thermostat in them, its somewhere else so it should be fine to put the ac there

Never seen it so I can’t say

I watch the show and he does get handsey with the stars and contestants but it might be a product of its time (many of the shows I watched were filmed in the 70s)