I have two under my belt now.
First was a broken screen, very difficult getting the screen off without leaving shards of glass attached to the adhesive. Replaced all adhesive with new.
Second was a battery that was expanding lifting the left side of the screen. Since the left side was lifted this made getting it started for easier. Screen came off intact. The speaker wire (Red/Black) is very fragile, I pulled the pins out of the holder when trying to remove. I was able to put them back. I would avoid it if you can as you only have to lift the mother board high enough to get the battery out and back in. There is enough slack, so I would recommend only removing if absolutely necessary. Followed tip to remove and replace thermal paste (Cleaner and paste (~$15). Had to replace the adhesive under the batter, just ran several stripes of the 2mm adhesive that I used for the display.
This site was a great guide.
My battery was expanding (Screen was lifting on left hand side) and that made this step the hardest part of the whole process. It was like there was gas between the foil and the battery inside, so it would pull away when trying to lift. You can use the iOpener and place under the section of the battery you are working on, that helped loosen it for me.
These screws were in a different area on my Surface, Pro 4 bought at release. The fan was visible and attached to the heat sink. Remove the two torx screws on the fan housing. No need to remove the Philips head screws that secure the fan.