IT is supposely said tt running the pump ext is abit cooler but by how much no ones has an answer.
I run all my pumps ext, but ensure there is constant air flow around/ past the pumps, cos they can get quite hot. So to reduce any sort of heat transfer via radiation/ conduction, having some cool air flowing past them pumps is good
As for returning to main tank: U can build a smallbuffer box like a betta bos at the outlet of the gate valve.
Have some sock / filter bag over the outlet and the betta box will be a back up for any bubbles tt escape. Allow enough time for the bubbles to rise to the surface, instead of dwelling in the water colume.
However, the sizing will be trial and error. And will take up some space in yr main tank. The idea is to slow down the water exiting the skimmer thus allowing the bubbles to rise to the surface like buffles in sumps.
my 2 cents