1] No, 406.3[D] says you can replace a non-grounding receptacle with another non-grounding receptacle. No on the TR also, since they donít exist in a non-grounding receptacle, as far as I know anyway. There is also the option of using a GFCI receptacle in place of a non-grounding receptacle.
2] That would be a yes, since the added receptacles are new work, not existing. They would need to be TR and also donít forget that if AFCI or GFCI protection would currently be required for that location, you need to address that as well.