On page 19 of the ethereum yellow paper: http://gavwood.com/paper.pdf it defines the address of a wallet as: A(pr) = Β[96...255](KEC(ECDSAPUBKEY(Pr))), which is the right most 160-bits of the Keccak hash of the public key generated by the private key.

If I expose the public key to the network, do I allow people to impersonate me and sign transactions even though they don't have Tr, Ts, or Tw? My understanding is no, that without those values you can't hash the transaction.

Subsequently, this leads me to wonder if the purpose of the address (besides identifying users) to obscure the public key so that the private key is at a less risk of being reversed? Or can the public key of any address be captured?

If the public key of any address can be identified on the network or off network (without actually being the owner of that key), how do you do that? Are there any resources on how to perform this that are computationally easy?