Soo paying a TX fee makes the transaction go through faster.
Non spam tx can be sent with 0 BTC and will be considered valid. Miners have the choice of including or excluding tx but almost all include all valid (non spam) txs regardless of fee.
In theory yes and someday that may be true. Today essentially all miners include 100% of tx in the next block (as long as they are not unpaid spam) even with no fee. So fee (beyond any anti-spam fee required) doesn't really increase speed.
Over time (as block subsidies decline) bitcoin will move to more of a pay per performance kind of model. I have started requiring fees for tx I process and hope other miners do the same.
https://bitcointalk.org/index.php?topic=73941.0Realistically though since he amount of fee is irrelevant for 99% of hashing power it likely will be a while before fees (or lack of fees) have any meaningful effect on confirmation times.