Both are grammatically correct, though I would tend to go with #1. “What” and “which” are closely related (and are sometimes used interchangably), but I see them as slightly different in meaning. Asking “which?” indicates a choice from a specific set of options, whereas asking “what?” is more open-ended. The sense I get from #1 is: “This car has 10 parts that need to be fixed. Which parts are actively being worked on?” #2 gives me the impression that the parts haven’t previously been identified: “I see your car is in the shop. What parts are actively being worked on?”
The reason I would tend to go with #1 is that the word “parts” implies that you are choosing from a predetermined list. Even in my example, the parts are limited by the “your car”. I couldn’t think of a good example using “parts” where I would pick “what” over “which”.
Here’s an example that is clearer as to the distinction:
“I like egg shell white or meringue white for the dining room. Which color do you like?”
“I don’t care what we paint the dining room. What color do you like?”