Making Prosciutto with skin off (Wrapping in butcher paper?)

The official answer is generally only a few days for meat in the fridge ...

Ham can be different, as it's salt cured, so depending on the salt content can last longer without freezing it.

As for freezing it, it really depends on how you plan to use it:

• It's most convenient to cut it up in the same way that you're going to use it, so that you can just pull it and use it easily
• For maximum storage time, the less surface area (larger pieces) the better. Diced ham will get freezer burnt much faster than just bagging a 1lb chunk.
• As with freezing most meats, you want to double wrap it to prevent moisture loss (and freezer burn).

So, I'd go ahead and ask yourself how you envision using it up, and how quickly. For instance, if you think you'll make a pot of ham and black bean soup in the next month or so, go ahead and dice it now and freeze it, and you can just pull and dump it when it's time. If you like ham steaks, slice them up, wrap and freeze those -- you can always chop it up further to fold into a casserole once it's thawed, if you have to. If you have so much that you think you're going to get sick of ham and need a break, freeze it in a large chunk ... but you'll want to give it a day to defrost in the fridge so you can actually cut into it when you want to use it.

Mortadella does need to be refrigerated.

As for the proscuitto ... if it's real cured ham (and not the fake 'cured' stuff you get in the US) and was trimmed with a clean knife and wasn't otherwise contaminated when being cut, and it's not the middle of the summer where you are, it's likely fine being stored in a cool area of your kitchen.

Mind you, the US FDA would't agree, and you would get cited for health code violations if you were a restaurant. You may also want to be more cautious if you're going to be serving the meat to people with compromised or otherwise weak immune systems (eg, small children or the infirm).