You probably could try rotating the mount slightly forward to get the mirror more above the handlebars and less likely to get bumped. I guess you could also add the stalk back on and get it more forward and way out of the way. As far as noticing until you need it, I feel it comes down to use case, and in my case, a glance or using it almost every minute of my ride. So if I bump it getting off the bike, which can happen occasionally, I notice as soon as I start pedaling again.
As for your available stability to use a free hand when riding and climbing to grab a bottle or adjust a mirror will come with time and practice. If you want to get better at riding with a free hand, you need to practice it, or you'll never gain the muscle memory. In my case, I drink with my right so I can steer with my left only quite well. In the less common times, I have to steer with my right hand to adjust my mirror or grab my left bottle to make the swap, I'm only half as stable. If I really wanted to prioritize better steering with my right, I should drink with my left, but the drive to do so ain't there yet.