Yes, this will fit the Trijicon RMR adapter plate that should have come with your pistol.
Yes, this will mount to the picatinny rail. The manufacturer does not provide a recoil rating.
Yes, this will be compatible.
This will fit a full size Glock MOS using the RMR optics plate. If you do not have a MOS Glock, then you will need a rear sight adapter plate, like MPN: 49513 which can be found here: https://www.opticsplanet.com/evolution-gun-works-trijicon-rmr-sight-mount-1-780-in-aluminum.html?_iv_code=KK-RMT-TRJRMR-49513
The red dot automatically turns on when there is sufficient sun light however, it does not have motion activation.
This does not fit the Kel-Tec red dot mount for the PMR-30.
You would need an RMR adapter plate in order to mount this on your pistol.
This unit comes with a Picatinny/weaver type rail mount, so it should attach right to the rail you have.
Yes, you would need a weaver/picatinny rail or an RMR adapter plate to mount this on your Ruger Mark IV.
Yes, you would just need a Trijicon RMR compatible mounting plate.