Installing and upgrading help

Pretty new to this and had a search around and needing help. Have Moodle setup on the Intranet and all goes well with a few courses. Want students to have access at home...questions;

1. Can you run Moodle from the one server both on the intranet and point to an Internet domain simultaneously?
2. Or do I have to have it point to an Internet domain and then have students go to that site to use on site?
3. If so (2) will this blow out our downloads or do I have to set it up to cache the moodle content
4. Of course if all of this is detailed elsewhere would be happy to be pointed there.

Many thanks in advance and sorry about the newby questions
Dan