you can say "ging" but that's normally only used in written form. Sounds a bit too formal when you say it. I would say "Ich bin nach Italien gegangen." or "Ich war in Italien."

gehen can mean "to walk" but not necessarily. You can say 'gehen' in meaning "generally going." So gehen does work in "Ich ging nach Italien."

I don't think it is. I think that the verb 'gehen' ('Ich ging' in the past) implies that you walked there!