Yes, in Italian Rovino means I ruin, though I don't think Hima might thought to use this name, since it's a verb and not a noun... (although Lovino destroys everything when does chores.)

Lavinia is quite used in Italy, Lavinio not much.

Well there are a lot of guesses about Lovino's name. Feliciano is a male name, but I've never heard about it, normally all names based on "felicità" (happiness) are Felice.

Anyway the only official thing we know is that Himaruya used non-common Italian names for Italy's brothers. Honestly I like them, it's true they're unusual, but I'm used to them by now...