Hi, Mark ~
Allow me to extend my welcome and regret that you've received a diagnosis of an acoustic neuroma. For the optimist, the good news is that this tumor is small, almost always benign and can be removed or irradiated. Acoustic neuromas are generally found in people twice your age so your questions are relevant, especially when considering your age (24).
I'm not a physician and I could be mistaken but I doubt that there is little you can do (or not do) that will effect your relatively small AN. It resides deep inside your skull and is not affected much by external forces, including amusement park rides. I don't see how exercise would make much difference, either. To the best of my knowledge, lifting weights or jogging won't affect a small tumor inside your skull. It is not an aneurysm, which can burst, often with life-threatening results. The AN is fibrous and usually has to be 'peeled' off of the sheathing of the nerve. It can't be dislodged by your activity. Flying can be a problem (as Phyl mentioned) for some but it shouldn't have much effect on the tumor one way or the other. That's more of a comfort/convenience issue for you.
At 1 cm, radiation (as a treatment for your AN) remains a distinct possibility in your case but you'll need to consult with doctors that perform that procedure, which is non-invasive (no cutting). Surgeons are often either disinterested in radiation treatment, uninformed about it's benefits and risks or simply won't consider it. You'll have to be your own advocate if you want the broadest range of options and medically sound advice. We can offer suggestions, but we're not doctors and can't make decisions for anyone. We do want to help in practical ways, though. That's what this website and especially, the forums, are all about. We inform, suggest and mostly, support other AN patients to the best of our collective ability.
It may encourage you to know that I underwent AN surgery, then irradiation - and came through it all just fine. I was almost 40 years older than you are now, when that occurred. The thought of AN surgery is definitely daunting but it isn't quite as scary as we usually think it is. Many have endured it. As Phyl mentioned, it's a minefield, fraught with risks. Some AN surgical patients do very well, some do 'O.K.', some not so good at all. There is no simple answer. We try to offer the best information available or, more likely, point you to it. You need to be animated to find the best path to follow in dealing with your AN so please don't become petrified.
Thanks for posting and of course, my best wishes and prayers for you as you begin your 'AN Journey'.
Jim