I know you're looking for self-hosted, and I hope you find it. But in case you don't, the free tier of calendly might do the job. I used to use it when I was job hunting.
No refrigerant. Just a stream of cold air coming from a vent on the unit.
Well, there's probably a refrigerant in there somewhere. But it's not like HVAC system with a refrigerant line and a compressor outside. It's all contained within the unit, and cold air just pours out. You can direct that using ducts.
No, I meant they hate you specifically. It's completely unjustified, but topologists are jerks. They wouldn't go into details, but they blame you for 'The Incident'.
I almost built that for my last house but ended up moving before I could. It wouldn't need much, just an extra pipe with a baffle and a door that opens internally.
Eh, not in comparison. Burning oil counteracts your AC, so both fight your HVAC somehow. And heat pumps are more than 100% efficient. I.e they can heat the water more than the amount of energy spent.
Oh yes. Let me get a copy of my birth certificate from the government to give to the government. No problem with that process. Very efficient.