Second, what if someone mined Wallets instead of bitcoins? What I mean by this is that if someone created a client that continuously created send and receive wallets how long would it take before all of the addresses are used up? How would you prevent this?
There are 2^160 possible addresses, so your investment in wallet mining to find a collision would be astronomical. You would not get any benefit from it --besides the big news-- as the only wallet who would be able to spend that address's balance is the one who has the private key.