He and I are having the same issue, after going to another server in which didn't have the mod our ships were turned to dirt. By uninstalling the mod and unlocking the FTL drive on my relatively new character I managed to get my ship back but both him and I sadly do not have teleporters. There is basically an invisible barrier where the teleporter should be.

Found the fix, you just delete your shipworld file (or if you have a backup from before the mod) and then relaunch the game, it respawns the ship as if it were chracter creation. Note: REMOVE ALL YOUR ♥♥♥♥ BEFORE DOING THIS, ELSE IT WILL BE GONE FOREVER.

I would try downloading the mod Flat Teleports, it adds in the MadTulip's ship telepoter programing and the 2 stop tele-shop sells them in this mod as well so you could just place that in the ship.

What Happens if I unlocked the first fake license and delete the shipfile? Will I only be able to get the second license and not redo the first; basically making the ship be cut in half?

Also... Where the hell IS the world stuff and all that crap I gotta access?

if you delete the shipfile, you keep the license, so it'll just give you a blank (whatever class you have) ship. To find these, go into the Starbound file on steammapps/common, it'll be in storage/player (if you have multiple characters it'll have all the files just tossed into that file, I organize it by date so you can just use the most recent character). Always make backups though in case of mistakes.

Yeah, I managed to find it today after brief confusion with the Giraffe and Koala build file locations.
I've fixed it thanks to you!