Will I be banned for using mods or skins

Concerning the TR_XXX.esm, you're most likely trying to use Tamriel Rebuilt (good choice!) Antediluvian Secrets, which requires Map 1 (Telvannis) as well, so I guess the latter has been forgotten.

Concerning the warning, this means that one of the plugins you are using was saved using a different version of the game main files, e.g. native Morrowind.esm while you're using the Morrowind Patch Project. You can usually ignore this, although you should at least once check whether you're accidentally using a Morrowind-without-Bloodmoon version of a plugin that also has a Morrowind-with-Bloodmoon version if you have Bloodmoon installed or vice vers.

If you want to get rid of the warning for good, you have to open the respective plugin's .esp file with the TES Construction Set (using your actual Morrowind.esm etc versions as base files) and simply save it again (keep a backup though). That should update the claimed dependency without modifying anything else.

I am unsure what the cause of the "unable to connect" problem was, but I have updated my TF2 dedicated server files and now the console does show text once it has started and I, and my friends from their own houses, can connect. I do know, however, the reason that the server was crashing on startup. I was attempting to start the server on a MVM map, none of which are shown on the in-game level voting.

Thank you to those who have read and devoted some of your time to try help me solve this problem, even though it was not a problem we could have solved.