I ran bike service departments in the 1970s and 1980s. There are plenty of jobs, e.g., wheelbuilding, I'm happy to DIY at home. Eyeballing derailleur hangers is not one of them. I was happy to pay a shop to align my bike's derailleur hanger after a teenage lout dashed out into the street (backwards and zig-zagging, playing tag) and ran into me.
Take it to a bike shop. Aligning the derailleur hanger is an easy job with the correct (expensive) tool and arguably impossible without it. They probably won't charge you much.
The "problem" of the chain coming off the largest sprocket while backpedaling is not a problem. It's physics. The gearset and chain are designed to derail quickly and efficiently. They'll do that pedaling forward when you shift (i.e., when the derailleur changes the angle at which the chain approaches the sprocket).
They'll also do it pedaling backwards in extreme gear combinations (i.e., with the chain approaching the sprocket at an extreme angle). Physics. (Some bikes have long chainstays or other characteristics that might diminish the likelihood of derailing resulting from backpedaling. I might even own one or two of those bikes, but I'll never know, since I don't backpedal.) (I also avoid shifting directly from first to reverse while my car is moving forward.)
Last, please don't use the largest two (preferably three) sprockets with the 50-tooth chainring. Yes, calling your bike a 22-speed is mathematically correct, but the drive train components will last longer if you treat them with respect, avoiding the big-big combinations (plural) and small-small combinations (again plural).
Last edited by Trakhak; 07-11-20 at 03:00 PM.