I would like to learn to play trumpet. But what I have found so far are video lessons online. My question is if there is something more advanced that would use microphone and with FFT etc. could give me feedback if I play right note, rigth timing and also if I play it clean. I believe this should be possible.
Honestly, just find a local tutor. The money you'll spend on subscription to apps, you're better off meeting a tutor once a week for 30/45 mins and taking it from there. Bad habits can be picked up easily, especially as an adult learner.
Smartmusic.com does exactly this. It's not 100% accurate and is mostly sold to school band programs but they've got a pretty cheap annual hobbyist subscription.
That may not help you a lot but there is for piano. I use Flowkey and the app does more or less that. I don't know if the sound recognition is very good, I use it with midi and not the microphone because I play with a headset.