Can I play ps4 game on ps4 pro even if the normal old ps4 has broken?

I bought a ps4 pro and before that I had a normal ps4 and had bought a lot of games on the old one via the psn store and also had very long game progress and my old ps4 is now broken and I can if I'm on the ps4 pro log on to my acc continue playing my games with the progress I made so far on the old broken ps4?

Yes of course

You can play all of the games by now, but your progress will depend on whether you have saved them on the console or in online storage.