Let break out your questions into a series of steps:
Step 1. How do I know if the account 'FNLN@gmail.com' has been taken?
This is the easy part - Send it an email. If you get back an error message giving you a link to this page (https://support.google.com/mail/answer/6596), then no one has taken that email address. Since your question states you've already tried this, and that you cannot claim the address in the normal fashion, we can assume the address has been claimed.
Step 2. How do I take control of the account if it is inactive?
This is the more involved part. Google tracks every account ever created in two ways. The first is an active record of your login, password, personal information, and all the content you have saved in your account. The second tracking method is a simple list of all the account names to verify there are no duplicates. When you create a new account, it bounces the requested name off the 'taken' list first and either accepts it (if the address is unique) or rejects it (if it is not).
Accounts on the 'active' list will eventually expire and be deleted if there is no activity for nine months. This prevents their servers from being overwhelmed by phantom data.
The 'taken' list, unfortunately, lasts forever. This permanence prevents you from creating an account, forgetting about it or letting it expire, and then someone else claiming the account and sending emails under your identity. It also means that after nine months, even the original owner cannot reclaim the account because all of the access data was deleted when the 'active' record was purged.
Step 3: Since I can't take control of the account, how do I know if it is active?
Go to Google account recovery (https://www.google.com/accounts/recovery?hl=en) and tell it you have forgotten your password. If the system takes you to a link allowing you to reset the password, then it is likely an active account. If not, is likely inactive and, for all intents, dead. Apparently there is short grace period between when an account is locked down and when it is deleted (https://support.google.com/mail/answer/1212172?hl=en&ref_topic=1669055), but either way makes little difference to your question.
If you think the other account is not only active but the other person is impersonating you, you have legal options. The first step of which is to contact Google directly and see if you can get the account shut down.
Step 4: How do I get my co-workers to stop sending email to the wrong account?
If you figure this one out, please let me know.