As for as the Lenovo goes if you select the under $500 and then in order of low to high you will run into either Intel HD graphics or Celeron CPU or a lack of Ram or CPU speeds. Ok maybe the ThinkPad E545 for under $350 but it's still not worth it to waste on a laptop to do what he wants it to do. However there all used so even though they've checked it you'll get a very very small warranty and if you want to get a extended warranty then it's gonna cost more. Even still there's gonna be a issue with RAM on that E545.
As far as OP's post about having a very good knowledge of laptops, that might be true but idea of a gaming laptop to play and I quote, "edit video ok an that can run games the most demanding game" says otherwise at a price range of $350. Refurb or not it's not gonna happen. Maybe somebody off the street with stolen property that's trying to make a quick buck is this possible. Do yourself a favor and lose the idea of a gaming laptop for $350. Matter of fact lose the idea of even getting a laptop for gaming, get yourself a desktop if you want to game and edit videos.
Editing videos needs a lot more then what laptops can offer but at a way high price. Only people on the go need this type of equipment and I don't believe you are.
GET A DESKTOP!
As far as the desktop with the AMD A10-7850k APU you still need at least 8 Gigs of ram as your APU graphics are sharing your system ram, so don't forget that. Or you can buy the suggested card and crossfire it.