afaik the notable thing is actually that the purrs help heal bone fractures, which is presumably something to do with vibrations helping the process along mechanically somehow.

But of course there's also just the psychological effect of having a purring cat near you, same thing as how people heal faster from stuff like acupuncture despite the process itself not doing anything, we just benefit from feeling happy and cared for.

One of it's purrrposes is to shake wounds and increase bloodflow. This is why cats sometimes pur after conflict; they're licking their wounds in multiple ways.

according to Google, cat purrs are at a specific frequency that somehow helps you heal faster

Yup

Depends on the cats personality, some will tolerate, others will kill.

wheekwheekwheekwheekwheekwheekwheekwheekwheekwheekwheekwheek

Some cats are grade A dingdongs!

Still love them all.

I can answer the second question:
Generally, hot-blooded mammals transform 90% of the energy they get from food into heat.
So using a cat for heating your room is about 90% as effective as burning cat food in an oven.

Here's some napkin math for where I live:
1kg of firewood has 4kWh = 4000 kcal
which is about equivalent to 1kg of really cheap dry cat food (mostly carbohydrates)

1kg of firewood costs about 40 cents
1kg of cheap dry cat food costs about 1,20€

So, cat-based heating is about 3.3x more expensive than burning pre-dried, commercially purchased firewood.
(all of these prices heavily depend on how much you buy in bulk, though. And if you care about your cat's well-being, you're gonna spend 2x more on its food)

normalize communal cats
why should people just have one or two cats when everyone could have 35 cats?

Nice, that's basically free healthcare.