Antiques shopping Rome
#3
Regarding "home accents", I suggest looking in hardware stores, too. Some of my favorite home items (drawer pulls, glazed flower pots, etc.) were inexpensive and bought in off-the-tourist-track home and hardware shops in Italy.
#6
Did you see the HGTV show Brian Boitano was in where he renovated an old house in Italy? They went to Milan to get things for that house. Maybe you can find the episode online and get the name of the place (or perhaps someone on Fodor's will remember). They also went to a flea market, but it was in Chiavari.