Can anyone tell me if I need to keep the thin pieces of metal with the points on them that are on the transmission tunnel? I imagine they were used to hold something in place originally but it seems to be getting in the way as I try to put down the new insulation.I feel like they are obsolete now? Should I just cut them off?

I believe you are describing the things that grab the carpet backing and hold it fast. If you notice FIAT didn't otherwise attach the carpets to the car (no glue, few if any screws) and it wasn't molded like modern carpets.

Thanks- I may try to keep them not sure they are crucial