Index fund prices are tied to an index, hence the name. If the DOW goes up for a DOW index fund that fund will increase in value proportionally. Vanguard gets paid for managing the fund.
It's not so much that you can exchange a share of an ETF for micro-shares of the underlying security, but that the ETFs themselves keep their assets in the underlying and if it gets out of balance professional investors will short one side and go long the other and make the difference -- a form of arbitrage.
Specifically, in the case of SPY, if the ETF was trading higher than the underlying, they would short the ETF and go long an appropriate number of shares of each of the 500 companies. The difference in the price is their profit. The very act of doing this brings the two prices inline and eventually you sell both sides and close the position for realized gains.
Brokers let you do these transactions atomically. Of course, for transaction fees alone, this is not a strategy available to retail investors.
This is correct; Authorized Participants are the ones who exchange baskets of securities. It isn't really possible for individuals to exchange shares directly with the fund manager, but that's not an issue because the secondary market prices are kept reasonably close due to the professionals. The amount you can expect to lose relative to NAV (the actual value of your shares) is around half the bid-ask spread at the time you buy/sell.
It also helps with tax efficiency since the creation/redemption process allows for shares with significant appreciation to be retired.
