tomtomtom123

The chain does look shorter than I would use, maybe add 2 more links, but I don't think it's short enough to cause serious problems, there "appears" to still be a bend in the RD, so at least it doesn't seem completely straight and fully extended. But the angle of the camera can be misleading so I could be wrong.

What I don't understand is:
1) how does the chain fall off to the right side, "outside", of the chainring when you're on the innermost 2 largest cogs? Wouldn't the chain be pulled towards the inside, and not to the outside, since the chain should be angling inward from front to back?

2) And how does the chain falling off the chainring cause you to crash? When the chain is no longer on the chainring, it's usually hanging off somewhere on the crank arm. Continuing to pedal does nothing. The freehub will just idle and the hub wheel will continue to spin.

So I don't know why your chain would fall to the outside of the outer chainring when you're on the innermost cog.

Anyway, back pedaling on the largest innermost cogs can sometimes cause the chain to shift 1 cog over outwards, as someone else mentioned. It's just the chain angle. If your chainrings were moved closer inward, it may reduce the problem a little bit if it really bothers you, but depending on your geometry, it might just be normal. If you want to investigate, you should check what your chainline is at the chainrings. On a road bike with 130mm dropouts, if you have double chainrings, the midpoint between the teeth of the 2 chainrings should be around 43.5mm from the centerline of the bike frame. (inversely if your chainrings are too far inward, pedaling forward on the outermost cog may cause the chain to shift 1 cog inward. jump back and forth between or rub against 1 cog inward.)

And I don't know what you mean about the skewer for the rear wheel not being true. The skewer doesn't move at all and the straightness of the skewer doesn't have an effect on chain alignment. The skewer might not be manufactured exactly straight, but all it does it compress the frame dropouts against the locknuts of the hub. The downward load from the frame transfers to the axle of the hub, not to the skewer.

Also, a hanger alignment tool isn't that expensive. I bought a cheap Cyclus tool for around $25 but it wasn't very symmetric, so I bought an X-tools (bikehand) rebrand which was better for $45. You can buy one and check your hanger and bend it before you attempt to bend your RD. I found that my Shimano RD cage seems to be angled slightly outwards, and some other people replied to a thread that I posted that it's supposed to be that way.