Can I use the Mona Lisa as my trademark?

Trademark infringement isn’t an issue in tourist Nepal, so that’s probably not going to be a factor.

Haven’t the courts ruled that a slavish copy of a work isn’t eligible for a new copyright? That would seem to cover most of the Mona Lisa postcards etc.

Yes, if a photograph does nothing but exactly and accurately reproduce a public domain work then it is not sufficiently original to be protected as an original and creative work of expression.

This creates an interesting sort of paradox, according to atleast one author:

Allow me to chime in with a quick ‘Thank you.’ Thus place is an incredible resource, not only for entertainment, but for intellectual recreation as well.