This magnifier's body size is 30mm. Most shooter's utilize magnifier's in combination with a primary optic such as a red dot or 1x prism. If this combination set-up is your intended use then you will need to know the central height of the primary optic and find a flip-mount that place the magnifier at the same central height.
Yes, this should be compatible with that mount.
MPN: 510003 does not include a mount.
Primary Arms does not provide the length of their Classic 3X LER GEN IV Red Dot Sights Magnifier. I would recommend contacting them directly for more information.
The Primary Arms Classic 3X LER GEN IV Red Dot Sights Magnifier features 2.64 in of eye relief. Because the rail is so far forward on the Ruger Scout, you most likely wouldn't be able to rest on the rifle properly to have a good sight picture. I would recommend using a rifle scope and mounting it as far back on the rail as possible.
The Primary Arms Classic 3X LER GEN IV Red Dot Sights Magnifier does not include a mount. It works with 30mm rings and magnifier mounts.
The Romeo 4H uses an absolute co-witness mount, so you can use the GG&G Flip to the Side Magnifier Mount, which can be found by using the link below:
https://www.opticsplanet.com/gg-g-flip-to-the-side-magnifier-mount.html
The Primary Arms 3X LER Red Dot Magnifier Gen IV will work with the Primary Arms Flip To Side Magnifier Mount, both in a standard height and 1.75" height, depending on what you prefer. You can find both mounts by using the links below:
https://www.opticsplanet.com/primary-arms-primary-arms-flip-to-side-magnifier-mount-standard-height.html
https://www.opticsplanet.com/primary-arms-primary-arms-flip-to-side-magnifier-mount-1-75-height.html
Here is a QD flip-to-side option: https://www.opticsplanet.com/leapers-utg-30mm-flip-to-side-picatinny-weaver-qd-ring-mount.html
The magnifier does not come with a QD mount.