Hey Horsewoman, welcome!
Yes, you can ship stuff home. Many people do this because the item is either to bulky or whatever. Personally, I haven't done it. I can't imagine it'll be a problem in either Italy or the UK. Lots of guidebooks give you details on what to expect when shipping.
So, I'd say plan on it.
As for your passport, the only time you really need it on yoru person is when entering or leaving a country. They'll ask for it, often times, when checking into a hotel, though. Personally, I leave it in my bag in the hotel, although I know some who carry it with them at all times. I think you're taking a greater risk of losing it doing that, than having it stolen from your room.
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"Life is not measured in the number of breaths we take, but by the places that take our breath away..."