Yes, when you’re in a tin tube 30,000 feet in the air at a temperature of around -32C you need some form of central heating. There’s a heating control dial in the food prep/service area where the crew hang out. They turn it up and down just like you’d do at home. They turn it up when they want the passengers to sleep after meal times etc.

It can have a pussy depending on its price.

Yes, you just wind the window down!

Yeah, most modern airliners do have some manner of climate control, oh and that little deal that you twist to be blasted with tepid air if that's your thing

Yes, with a few exceptions.