Hi Max, I could write an answer as long as your arm.
For questions like this, yes it's always helpful to get teacher input, but your best bet is to have a teacher, and to ask them directly and to bring up specific scenarios. You can approach the way you practice piano in so many ways, that you are likely to receive an equal amount of yes - do exercises for specific problems as much as you would receive - no , just practice the pieces.
The reality of it is, if you practice just pieces you will eventually gain the skill and learn the piece.
However try this with pieces out side your ability and you can pick up bad habbits and make it very difficult to polish the piece and you'll end up having to leave it completely and come back to it.
Exercises don't practice the piece, but also don't destroy it if you're out of your depth. Having a teacher, can assess the right balance for you. You're unlikely to get a full explanation on here that will leave you 100% sure of how you want to progress.