I have a few simple questions.

My group is under the assumption that you can: add to your fleet supply with logistics/status phase command counter allocation. Is this correct?

Also, is there a maximum number of counters in the fleet supply pool that you can have?

Your group is under a correct assumption. Whenever you gain Command Counters (CCs), you may add them in any combination to any of the three areas on your Race Sheet.

As for the second part of your question, the limit to how many CCs you may have in your fleet supply area is 16. But having such a large fleet supply would hinder your movements throughout the galaxy since that is the total number of CCs any race have.

Hah, to see a faction with 15 fleet supply and 1 command counter aka, "The Big Red Button" strategy.