Can I use a silver jug for hot drinks?

Many silver jugs handle hot water well. You just need to check if the handle has heat insulators made of ivory or wood to stop you burning your fingers. Silver conducts heat rapidly. If it lacks insulators, the maker might have intended it for milk or wine instead.

I recently inherited a heavy ceramic jug that has some dark staining inside and a few small cracks in the glaze, so is it safe to use for water?

Crazing in the glaze allows liquid to seep into the porous earthenware body beneath. That is what causes the dark staining over time. It is better to avoid drinking from vessels with crazed interiors. Bacteria can sit in those micro-cracks. You should use it for flowers instead.

What is a mask head jug?

This term refers to a spout formed as a face. Factories like Worcester made mask jugs in porcelain.

If I buy a copper jug to keep on my washstand, does it matter that all the tin lining has worn away on the inside?

It only matters if you plan to drink from it. Bare copper reacts with acidic liquids and can cause illness if ingested. For a washstand display or watering plants, the missing tin poses no problem. Many collectors actually prefer the look of the worn copper interior on these pieces.