On DX, that 35 is like a 50, and it's a good walk around field of view. The 50 becomes too tele for lots of general stuff, but not enough for proper reach, so I'd honestly skip it altogether on DX. 85 would work nicely for portraits and is far enough from the 35 to merit a purchase IMO.
On the compatibility- 5100 can take absolutely ANY Nikon-F mount lens, period. It will only auto-focus with AF-S lenses with built-in motors. It will only meter with CPU lenses (that have those electronic contacts).
So, you can buy and use ANYTHING on the market, but for 70% of those you'll have to learn how to shoot "film" as the camera will tell you nothing aside from the focus indicator. Great learning tool? Yes! Useful in fast-paced environments? All depends on how good you become.
IF you ever choose to go the manual route, I'd highly recommend getting a split-prism focusing screen to make your life of manual focusing much more bearable.