The side shot with the GoPro takes the cake IMO. Also depending on what phone you can get a crisper image with side shot. You can also edit your videos and share them right then and there. I love your Wildcat, that's my next airgun. I want to use it as a truck gun.
I don't see why not, only thing that might cause a problem is the short eye relief and the recoil of 308 powder burner. Yes they fit most scopes, video quality is good once tuned too the scope.
I bought the Tactacam 5.0 and found the video quality to be horrendous... Definitely not even close to 4K. I'm in the process of ordering the EagleVision... Have had many GoPros over the years and their video quality is outstanding
I have found the Eagle Vision with Go Pro 7 to be better as long as the lens is good. Eagle Vision sells two, one is cheaper than the other by quite a bit but the cost is worth it.