Third-party app using the Traccar API

Is it possible to integrate Traccar notifications into a third-party app using the Traccar API? Additionally, is it feasible to integrate all Traccar functions into this app, which manages various tasks such as fine payments and car washes, among other things?

I don't see why not. It should be possible.

Is it possible to achieve this through professional services on your part, Anton, with the corresponding pricing, of course?

Depends on what technologies you are using, but usually the answer is yes.