You can have more than one global catalog, that should not be a problem.

As far as I know it is impossible to host parent and child active directories on the same box.

We have a site which has an unstable connection as well, it is on the list of things to fix, but not high priority as they do not complain very loudly.

They have a copy of the global catalog on their server, and can log in just fine.

As far as I know you cannot make a read only version. Since in Active Directory, all domain controllers are equal, there is not really a primary/ and backup. Though there are some single master operation roles which are owned by a single dc.