Runtime databases cannot link to a hosted database as a client so that approach is not an option. If you intend to pass out separate copies of the database that do not need to link to the server, that you can do, but if each of these copies is used to collect data to be synched back to the server, you'll need to plan that one out carefully as this is not a trivial thing to undertake even if you take advantage of a third party supplied synch tool.
Secondly, should I make one giant database, or break it down into two, one for each department.
There's no straight forward simple answer to that, but the more data that needs to be accessible to both departments, the more advantages there are to a single database shared by both.
Thirdly, is it a simple process to produce reports from one or the other database containing information from both database files?
If both databases are hosted on the same network, then it is quite easy to do, but if you are going to do that, your design and implementation are likely to be simpler if you just keep all the tables in one file, or set up a data separation system with two files--one functions as the interface and the other stores all the tables.
Keep in mind that security settings can be used to limit each user's access to only those layouts, tables and records for which they are authorized.
Thank you for your comments. They are of great help moving forward!!!