I am almost there to starting my click-lock floating engineered floor installation. Just one more question (or two)

1. how to intall corner round and reducer? nail or glue? if glue, what type?
2. I need to cut off my existing carpet in living room, but leave the bedroom untouched. Now living room and bedroom are sharing one big heavy broadloom (at least visibly one piece). How to trim the carpet in the doorway? do I need something special to fasten the carpet down to the concret so that it will not loose? what type of modeling do i need (t-modeling, reducer, or carpet reducer)?

thank you.