Generally speaking, yes.

Steven, it depends Sir. Weight is a big factor. A heavy 12 gauge may seem to kick less than a very light 20 gauge. 20 gauge shotguns are generally lighter in the same model so the kick difference is not as great as most folks think. I would go with the more effective 12 ga with a low recoil load or a recoil eraser : amazon.com/Recoil-Eraser-Slip-Filled-Black/dp/B08DK41RYH

Yes, and a 20Ga will kick harder then a 410, there are things you can do to mitigate recoil with a 12 guage, such as using a buttstock/recoil pad a d low recoil ammo, and training.

Yes, generally speaking, the same type of 12 GA ammo is going kick more than the same type of 20 GA. Unless you are shooting heavy load slug or magnum shotshell, I found 12GA with a good recoil pad really easy to manage even for small frame woman. I hope this helps!

12 gauge is a larger diameter shell with more room for propellant and projectiles and will generally output more muzzle energy than a 20 gauge and therefore "kick" more. But actual felt recoil depends on more factors such as the gun's weight and handling characteristics, the operating system of the gun, and the actual loads being used. A heavier shotgun will recoil less than a lightweight one using the same ammunition, a semi-auto shotgun will generally recoil less than a pump or single shot with the same ammunition, and birdshot/target loads will generally recoil less than heavy buckshot, slugs, or magnum loads of any type. But to a well-informed shooter with some training and practice either gauge should be entirely manageable.