These are shops selling food, cosmetics, house-cleaning products:www.veganhome.it/negozi/alimentari/lazio/roma/
Shops selling cosmetics only www.veganhome.it/negozi/cosmetici/lazio/roma/
Shops selling clothes: www.veganhome.it/negozi/abbigliamento/lazio/roma/
Be careful: most of them don't sell ONLY vegan and cruelty-free products, the sell ALSO vegan and cruelty-free products so you have to check everything you buy.
Here. some "vegan friendly" places to eat: www.veganhome.it/ristoranti-locali/cerca/?provincia=184
Again: most of them are neither vegan nor vegetarian, they are places where eating vegan should be easier.
They are grouped in:
"Ristoranti/Pizzerie" restaurants and places where you can eat a pizza
"Bar/gelaterie": ice creams, coffees etc.
Somebody living in Rome will probably give further advices.