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Those are some cute characters! The sound also fits and being able to choose between the different styles in the beginning felt really cool.

Something I encountered was that at a certain point on the map, I got teleported back to the last flag without any apparent reason.

it's because you touch the spike!
if you touch the spike you will die and respawn at the last checkpoint which is the last flag you touch. 

Ohhh, so those are the green spikes. I thought they were just for decoration :D since I could just walk past them before (because of green color) did nothing

Yes, those are the spikes, if you take the green paint you will get a buff to become immune to any spike damage!
I hope this explanation helps you :).