How feasible is it to reuse the bricks when rebuilding a wall?
When someone says something isn't feasible, they usually mean "I don't have the skills", or "I can't do this cost effectively", or simply "the job looks unpleasant. Of course bricks can be reused if they're not disintegrating. It's simply a matter of whether you really want to pay for that outcome.

That said, it's probably not cheaper to reuse the bricks. Bricks are cheap. Time spent disassembling and cleaning bricks isn't (if you're paying someone else to do it). The reason you'd reuse them isn't cost, but outcome. New bricks obviously don't look the same as old ones. 

The answer to your question, at its essence, is yes. You can reuse bricks. Humans have done it for centuries. 

P.S. I love that you posted the damage to the wall and the car.