A while ago I got a Borg officer and obviously I only get one so I can't have multiples, either on the one character or others.

If I dismiss her, do I lose her forever or can I hire another Borg character on another character?

The Borg BO is an account wide unlock, and can be claimed by any qualifying character... (Fed get the human Borg BO, KDF for the Klingon version)

If the BO gets dismissed, you can reclaim a new copy, limited to a single copy per character...

So ALL my characters can have ONE?
Maybe I'm looking in the wrong places, but I can't seem to find such an option with my other characters.

C-store bride officer unlocks can only be claimed once. So, if you dismiss your Borg bridge officer, you won't get another for free, it says this in the item description:

Look under the Legacy Unlocks section. If you bought the Fed Liberated Borg BOFF then all Fed characters get one.

Bridge officers are no longer account wide unlocks. They were pre-f2p c-store that is why they had the sale and stated to buy stuff before the f2p c-store went into effect.

When did you buy the borg bo? If you purchased it before they put in effect the f2p c-store, it will be an account wide unlock look under the legacy tab like others have said. However, I am not sure but you may only be able to claim it once per character.

Hmmmm, looks like they changed it... Though if you have a 'Legacy Unlock' of the Borg BO (like I do) then this is the original version that is an account wide unlock....

I bought it long before it was F2P. Like, 5~7 months ago?

Do I just pick 'em up (assuming I can) at the regular officer shop?

I have both Borg and Photonic BOFFs listed as Available under my Legacy tab on the in-game C-Store screen.