ACH is a reversible payment method. (Harder to reverse than credit card, but still an ACH payment can be reversed, such as the account owner claiming the transfer was not authorized.)
As such, there is currently only one exchange that accepts ACH transfer, Coinbase. They are able to do so because they believe they can automate the risk calculation to where that payment method can be accepted profitably.
Nope. That's not how ACH works. There are some online banking services which allow person-to-person transfers, but none of them work with any bitcoin exchanges [Edit: Except for CapitalOne 360 /ING, which you can use with BitFloor, but that's still not going through the ACH network].
Instead you log into Coinbase and link your bank account. One way is to give them the username and password to your bank account (for "instant" verification) and they have a process that does a look see and if all checks out, you enter their "probationary period" where you are allowed to buy up to $100 USD worth of bitcoins per day. [Though your transaction could still get cancelled at any time before delivery of your coins.] If you instead choose to do "deposit" verification, they send a couple deposits and a few days later after that happens you then tell Coinbase the amounts that they sent you, and that verifies that you own the account. Still only gets you the probationary amount of $100 per day. After 30 more days you exit probation and can buy up to 100 BTC at a time.
You are dealing directly with Coinbase, there are no other parties involved.
If you are wondering about other exchanges, almost none are person-to-person markets. The problem with those, as you can imagine, is that the seller doesn't know if the buyer can be trusted.