2 quick questions.
#1 If a Pokémon reaches a level where it's supposed to evolve, will it?
#2 If a Pokémon reaches a level where it's supposed to learn a new move, and it already knows 4 moves, will it make room for the new one?
No they don't. Had it happen for both. You have to level the Pokémon once more in the cartridge for it to evolve/learn the move.
And @Blazaking EX Noooot really. :/ Unless you're ready to constantly be sending it back and forth between the cartridge and the Pokéwalker, it's not really fast. I tried to do this for my Pidgeot and it really just didn't work well speed-wise. It's a good supplement, but unless you're ready to constantly be sending it back and forth, don't expect it to be fast (Plus, after a while it needs more exp and as such needs more walking time to level and blah blah blah).