yes
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You'll need to wait until you catch at least one other Pokemon, then store it in your PC. Save then restart, in the main menu go to "Connect to Pokewalker". Or turn to pg. 52 in the instruction booklet and read the part that says How to restart your pokewalker!
Yes, unfortunealy, they will.
Resetting the Pokewalker doesn't affect Routes; they are stored on your cart.
Yes, while a Pokemon is in the pokewalker it is unusable in the game until it returns. The pokewalker is also only capable of taking Pokemon out the PC, so you need access to one. If your pokewalker is lost or stolen, look in the game's instruction manual to find how to force it to return.
There may be a few reasons, but you will probably need to reset your PokeWalker. The instructions are in the instruction booklet that came with the game.