In the simplest case, an order book is generated from all outstanding buy and sell limit orders, assuming none have crossed (if they have, the matching engine will immediately transact those orders). The price is discretized, so there is a minimum tick size, and each price has a FIFO queue of orders.
HFT provides liquidity to all other traders, including other HFT. They are paid in either the bid-ask spread (in the case that HFT is passive) or arbitrating bid-ask spreads between different exchanges, e.g. they aggress and take out an offer on exchange A which is below the bid on exchange B, providing liquidity to the standing offer on exchange A immediately instead of letting the prices disjoin.
The answer to the last two lines are the same -- there is no meaningful difference between a buy and a sell. The net effect is more liquidity than without any short term market making, for both market and limit orders (IMO market orders should simply not exist, but that's a small aside).
What's the mechanism for matching buyers and sellers?
Does HFT provide a benefit to the HF trader? If so, from whom does that advantage accrue?
What's the net effect on a non-HFT buyer with and without the presence of HFT? For market orders? For limit orders?
What's the net effect on a non-HFT seller with and without the presence of HFT? For market orders? For limit orders?