What does your mileage have to do with it? Do you get the first three oil changes free from the dealer? I changed over to synthetic at 3k miles and always do my own oil changes. I don't need/want some stealership doing anything to my van unless it's free warrantee work!
I don't know. I never heard that before but if you get four free changes I guess I'd take them.
I know a lot of cars come with synthetic oil from the beginning. The only real reason to use it in my opinion is if you can buy it for cheap (under $4 qt) as it's supposed to go 10k miles between changes and doesn't hurt!