The failed component in the first picture is the 12V regulator. It feeds 12V to the TMC5160 gate driver supply, as well as the 12V fan supply. If it has failed with a short circuit between input and output, then it's likely that all the TMC5160 drivers have blown, and possibly the output mosfets too. But if it has failed open circuit, then the board can probably be salvaged by replacing the burned components.
The second photo shows what i suspect is flux residue, probably the result of some manual rework of the soldering of the SD card socket pins. It can be cleaned off using a cotton bud and IPA.
If you provide USB power only to the board, are you able to communicate with it? Do any of the TMC5160 chips look damaged?