To answer the question on modability. The game is VERY modable, one of the most modable games out there. The API is vast, with something like over 200 class objects to uniquely modify the game experience, and another 200 core/example class object implementations to say nothing of the number of methods and attributes that can be modified in real time.
There are numerous types of mods people have made, from overhauls that make the game with Star Trek or EVE ships and weapons. To re-creating something massive like Star Control 2. Some enhance the vanilla experience with Uomoz's Starsector or Starsector+, or significantly overhaul the game visuals with Shader model GPU effects as with Starsector+ with ShaderLib.
Then there are crazy/strange things you can do, someone created a Nyan cat ship with a rainbow engine trail, I think there was a dubstep beam weapon (which was cool) and a there are a whole bunch of features, weapons, and dynamic special effects people have created that are too long to even list..
A personal favourite of mine is the Starsector+ arcade mode, changing the game from an RTS combat game to a fully fledged arcade with dynamic and randomly created ships that increase in difficulty in level, mook types, a score counter, power ups and unique bosses that spawn at various stages with unique weapons and abilities.
It's a better question as to what can you not mod in this game, and right now, that isn't a lot.