Piyutim

This YK I davened at KAJ-WH. I had difficulty figuring out when the tzibur should ONLY respond to the chazzan during the piyutim and when the tzibur should recite the entire piyut. Some clarification on this would be helpful. For example, during birchos krias shema we say baruch shaim as a refrain. I ended up reciting the entire piyut as I was no where near the chazzan when he got to that point. However, should I have been up to the chazzan, would it not make sense to recite the entire thing as it is in birchas krias shema? To take another extreme, when the piyut of marreh kohen is recited, it seemed obvious to me that the tzibur should only respond. Another point, if the chazzan is going too fast to say the entire piyut, what should one do? This can happen in birchas krias shema and during the long extended kedusha.

Would such advice apply even to piyutim said during krias Shema?? I would assume that if one has a basic general idea what the piyut means, even if one does not know all the specifics, that it would be better to say it in Hebrew. True?