How To Tell If Derailleur Cage Is Bent. You can eyeball the derailleur cage alignment by looking down the chain-line from the back of the bike - see image below from this question. If you find that you cannot find a balance between perfect upshifting and perfect downshifting through cable tension then your derailleur hanger may be bent.
Having a spare derailleur hanger on hand is always a good idea and its something that I make a point to purchase with every new bike. Once bent the derailleurs and pulleys are not going to align with the sprockets. I wont recap this because if these steps are foreign to you it might be best to bring your bent cage to a bike shop.
Peter wants to know.
Any time your chain gets stuck in the spokes at speed faster than average walking speed you can say goodbye to your derailleur. I cant say the derailleur is bent looking at the photos but I can say if the replacement cranket top ring is a 52 teeth or 50 teeth size then it is more likely a crankset mismatch to the front deraileur since the max teeth it can handle is normally 48 teeth which is why it does not curve to a road cranket of 5250 teeth. It must be parallel to the cogs. It wasnt clear whether the derailleur cage was bent or if it was the hanger everything looked pretty normal.

