As my collegue already said, thanks a lot for your feedback! I was mainly responsible for the platforms etc. and I knew they weren't perfect but in the end there wasn't much time. As to answer your question, it didn't have anything to do with the player material but the physics material attached to the platforms. Also the player couln't move because I made it the child of the moving platform -> so it's position updated with platform. Maybe not the best method:)
I mean hey, at least it works well enough to complete!
I think that is the right method; at least it's certainly better than what I did in the past! After a brief look around on tutorials, it seems that setting the player's parent to null when moving horizontally (on the player logic script) might fix this issue (with an added "OnCollisionStay" to reset the player's parent to the platform on the platform's script). Hope this helps, I know it helped me for future projects!