Depends  on the lease and what the plumbing problem is.  Stoppages in a fixture are normally the renters fault 

Yes, usually by the color as lead will oxidize faster

You may want to protect the fixture traps from freezing by pouring in  approved anti freeze  and also make sure that all trap seals are replenished before leaving to prevent carcinogenic  and flammable sewer gases from entering your home

The Correct answer is  as follows

If you have cats or little kids in the home AGAINST the wall so there critters don't pull on the paper

For adults then have the paper facing away from the wall to allow for easier access  

As a NYC Master plumber and expert witness this is the correct answer

Actually it depends if you have a cat in the home  or little kids,

If the home has adults the roll should be  away from the wall to grab the paper easier If children or cats are then then you want the paper against the wall so  the cats - kids don't pull on it