Can we export our recharter data into a file that can be transferred to the BSA?

Unfortunately, this is no longer an option.  The BSA has apparently discontinued it's ScoutNet Recharter Upload function, which TroopWebHost supported with a corresponding export capability.

Please contact your BSA representatives and urge them to create a file transfer capability in the new Internet Advancement recharter page.

My site is shared by two scouting units.  How should I use the TroopWebHost recharter function?

The TroopWebHost charter function was not designed to handle multiple units.   You can either process each unit's recharter separately, in which case you will have to replace the members from the first unit with the members from the second unit on the second pass.  Or you can process them as one large unit, in which case the recharter worksheet will show the members of both units.  We understand that neither of these approaches is ideal.