Some rifles I cant, some my elbow is up, and some is as you describe. I make the rifle fit me, and not me fit the rifle in most cases
I basically do the same thing. The first thing to go is usually the recoil pads they seem to think we need. I also try to keep all the LOP's to right around 12 1/2"-13" so everything is as close to consistent as possible.
As far as elbow up or down, that usually depends on the type of stock. Stocks with a detached pistol grip, like the AK or AR, I usually shoot with it down, where I usually have some variation of a chicken wing with a more traditional stock.