Does anyone know of Mods that transform this game into an open-world, free roam simulation? I would LOVE to take my crew and conduct exploration, trade runs, join in random battles, get fleet orders, etc.

That would be my dream game TBH.

No such mod was made. They would always focus on the quick battle and multiplayer modes, alas.

The closest you'll get to your description in Trek games would be Star Trek Online and Bridge Crew, I guess. The Starfleet Command series would sometimes give you a scan mission but would eventually end up in combat anyway.

Search for Bridge Commander Galaxy Charts

There is a galaxy war mod - basically you get a lot of systems and when you warp im random ships will show up - its quite buggy and so unreliable and doubt it will get fixed and buggy means it crashes to desktop. There is nothing with free roaming non conflict type missions.