mtb qr skewer / stunt pegs compatability

That’s fine, pretty standard. My skewers are 4.84 mm

Usually the trainer comes with a skewer that has domed ends on. I’ve used one on everything from a kids mountain bike to an adult road bike, so the axle length is not a problem. There is a mating clamp on the trainer that docks onto them, so the axle is held at each end. The trainer should come with some device to allow it to fit different wheel sizes. 

You will want to get a turbo tyre. A standard MTB tyre will make an entertaining noise and spray rubber up the wall.

Check the skewer thickness precisely. I got a ‘bargain ‘ wheelset once that only takes a really thin skewer.  

Plenty on ebay- get a second hand one and you can look up the manufacturer’s spec on their website. 

DC Cycles does a pretty decent Warm Up Stand. We got one which we take to BMX race events, to warm up before races. My son uses it to balance his GT BMX racer on, though I've also put my own GT BMX racer ont it as well. It has quite a range of adjustability. It's nice and stable in use and quite well made.

https://www.dccycles.co.uk/index.asp?function=search

You might want to contact DC and see if it'll fit your MTB, or if they have something similar that will.

Probably better off getting a turbo trainer - you should be able to pick one up 2nd hand that would be in your price range.  This will give variable resistance, and will likely me more stable.