Good question about fighter bay and I noticed that there is only minor mention in tutorial when freighter hull has been received. Fighter bays give ship certain amount of bay space. This can be used for loading small and medium ships into those bays. Small hulls require one space and medium require two spaces.
Idea in fighter space is that you can have bigger ship with fast FTL engines on and smaller ships can use those nuclear engines which are really good in combat. You can design freighter full of fighter bays with fast engine on it to travel big distances. Then you designs for example Corvettes with nuclear engine, since those have slow FTL you simply merge those into same fleet. Now whole fleet travels with speed of that freighter in star map.
I'll make a ticket where fighter bays are explained. I could actually add explanation into research view what each component actually does.
Auto-combat is planned for 0.19.0Beta version. Order which ships are place in combat that should be easy to do. Formation are a bit harder since ships are placed in three rows. Third row is used if same sector has also a deployed star base. Maybe some kind of automatic order would be fine where non military ships would be placed on behind and allow player to select if small or big military ships are preferred to be on first row.