2. Bluetooth works fine. I haven’t ever needed to re-pair my Bluetooth keyboard to my Mac or iPad
3. The iPad works with any random Bluetooth keyboard and mouse. Bluetooth keyboard support has been available on the iPad since 2010. Bluetooth mouse support has been available for 7 years+.
If you have problems with Bluetooth keyboards, that says more about other operating systems. I’ve used them since my G4 Mac Mini in 2006.