Only user specific tables should go in the fe. Not sure I understand the rest of the question(s) but ODBC linked tables are not copies of the source table in the sense that they are table defs in your database. They are just links.
You can keep a connection open by opening a select query on the be tables, but you should only do it to one table. If your connected tables are very large, consider having native be tables that only contain what you need. You can do appends and updates to them on a regular basis; I used to do this nightly via Task Scheduler.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.