No as those side effects are not recoil. Recoil is only if the attack lowers the user's HP.
4th Gen games cannot connect to Black/White over wi-fi, only through local wireless, and it isn't a direct trade, it is sort of like Pal Park.
Fossils are in the desert cave. Go in the cave, go all the way left, walk over the sand trap and talk to the NPC on the right. I think the turtle is the first option, bird is the second.
To revive the fossil go to the museum where the 2nd gym is located and talk to the receptionist on the right hand side. You will need a spare slot in your party to receive the Pokemon.
Town with the 4th gym in it, one of the houses above the pokecenter
Thanks. I should always talk to every NPC. I can't believe I was at Champion Road with no HM4.
Though, it's not "above", it's northwest.