Hi there - as far as your original question - I think everyone's pretty much answered it but, being a boxer lover, I have to put in my 2 cents (hope you don't mind).
1st - Renee750il was so right...boxers are farters, loud stinky ones. If your mom's wanting something to show off that might be a problem. Mine's embarassed me more times than I can count (however on a positive, I was playing a game of pool w/my dad one day and it was down to one shot and Tyson let a HUGE one and made dad miss so Tyson won me the game!! maybe it's not all bad - lol)
2nd yes the love exercise but not just the same thing over and over. running is good but they get bored easy so they wouldn't be happy doing it for very long, they like a change of scenary like every 10 seconds - which goes to my next point...
3rd again they get bored easy. They're sharp as tacks but you have to be patient when training. 5 min a day 3 times a day everyday is about it. More than that and they're apt to ignoring ya more than listening.
4th although they love exercise ("play") they also love being a couch potato & a lap dog - all 65 lbs/they don't realize their size usually - that's just part of owning a boxer
5th they are clowns - happy go lucky clowns that love people - especially kids. I actually saw a report in a boxer magazine almost a year ago that said that out of every recognized breed in the world, boxers were the 3rd top rated dog to have for children (beat out by labs and something else I can't remember). As far as adults, usually unless trained not to they will immediately run up to them for attention and want to lick and hug them. Very affecionate dogs
6th occasionally you can get one that is dog aggressive but not usually - not at 1st anyway. I've noticed with ours, they (well not Princess) but Tyson & Bentley love other dogs but also annoy other dogs by playing and following they around and licking on them. As soon as the other dogs gets annoyed and shows it by snapping at them or growling then that's when they get defensive and that can become dangerous. Princess has to be the dominate dog so she's not a good example really and Tyson is a scardy cat so he runs and hides but he will fight back if threatned long enough.
7th on the shedding thing - well mine are exceptionally "sheddy". I have to sweep daily and vaccuum every other day - do laundry after a good snuggle fest on the couch (or itch from hair the rest of the day). Also Tyson has severly dry skin that we've been trying to control for months to no avail - not good for anyone with bad allergies. Dry skin, bloat (due to such a deep chest) and joint problems (due to activness & love of jumping) are all things to be aware of with boxers.
I know this is like a book and a lot of it has already been said but it's just general rules of owning a boxer.
Good luck finding the right dog!!