Multiple objects and parts of an object using same texture.

I want to ask this before I work on character models so I know the most effective way of doing this.

If multiple objects use the same texture, does it load into memory once, or once per each object?

If a single object has multiple parts (because it's modular, and various portions are shown or hidden depending on the state of the object) am I better off putting the parts that are related into one file or as separate textures one per part? (for example, a characters skin would all be related and I could put the head, torso and limbs onto one file even though I may hide the torso to show armour, but the armour would still have to be separate textures depending on what the character is wearing.)

If multiple objects use the same texture, does it load into memory once, or once per each object?

Short answer? It only loads the texture once.

For the second question:

Whatever you're modelling, using a single texture for multiple parts is the best way to do it (where possible). This is known as a texture Atlas.