Yes, the internal specs are the same as Gen 3 Glock frames and TacSol states their kits work with Gen 1-4 Glock frames.
No, the Glock 44 magazines will not be compatible with the Tactical Solutions TSG-22 Glock .22 LR Conversion Kit. You will need to use the supplied magazine.
No, you cannot use a Glock 44 barrel in this slide. But they do sell a threaded version: TSL-CNC-T1G-TSGCON-19-TE-10RD
Yes it will work on your Glock 22 Gen 2 and everything needed to function, is included with the kit.
Swap out the factory upper assembly with the TSG-22 upper assembly and a TSG-22 magazine and you're ready to go.
The TSG-22 Glock conversion is designed to fit Glock generations 1-4. Tactical Solutions does not have a Gen 5 compatible conversion at this time.
The TSG-22 GLOCK conversion is designed to fit GLOCK generations 1-4. If your 80% frame meets that spec, it should work.
The recoil spring weight is specific to 22LR. I would suggest contacting Tactical Solutions directly, as I've been unable to find just the recoil rod/spring.
Yes, you can find that here: https://www.opticsplanet.com/tactical-solutions-tsg-lr-22-10-round-magazine.html
Per the manufacturer, no it will not fit Gen 5 model Glocks.