I wouldn't worry about the fender. They get bumped, knocked, stays get out of adjustment, etc, all the time, and the way to fix it is to just tug the stay back into place. I suspect that what they told you about the quick release was because they assumed that the wheel wasn't all the way in or something.
As far as the shifting issue and the brake rubbing, that should have been adjusted and it should only take a few minutes. It sounds like someone just dropped the ball and forgot, or someone did it who wasn't very good at it. Stuff falls through the cracks sometimes, especially if the shop is just starting to get into their busy season. If you call the shop and tell them about it, they should just tell you to come by and they'll adjust it for you, and it shouldn't take a long time. If you can come by at a time that's not busy (i.e, not a sunny saturday afternoon) they should be able to do it while you wait, or nearly. You don't need to accuse them of selling you a shoddy product or not doing their jobs or anything; just tell them it's not shifting right and they should take care of it.
The rear rack needing to be removed is understandable if they put racks on their rentals, since racks cost $$ and they'll probably just put it onto another rental bike.
The wheel being a wee bit out of true is about standard for a bike in that price range, particularly a used one. It's not a problem unless spokes start breaking. It will be fine. But even if you do start breaking spokes, that's not really anything that the shop could have predicted or prevented short of putting much more expensive wheels on the bike. Although if the variance is really 0.5mm that's pretty decent anyway.
As far as the manual goes, you don't need it. It doesn't say anything useful, and the shop probably tossed it out with the packaging material the bike came in. The only time anyone cares about the manual is if it's some special vintage item where having the original manual is cool.
Usually, bike shops include a certain amount of service when they sell new bikes, which basically means adjusting shifters and brakes after the bike has been ridden a bit. Policies vary more with used bikes, but I wouldn't get too bent out of shape about this case unless they refuse to fix it or try to charge you for a tuneup.