this whole thing about shield mitigation and focus fire.
shield mitigation will scale up as targets take damage at a rate proportional to incoming damage. mitigation drops off at a strictly linear rate, which is independent of incoming damage and constant. i won't get into the exact math of this, i probably don't have my figure totally correct so i don't want to say something that isn't mathematically accurate. you'll have to forgive the vagueness and just believe that this is the general outlay of how it works.
the way the system is implemented it is by far preferable to focus fire. you might think that because of the linear constant drop off of shield mitigation you would gain more from spreading your fire around but this is incorrect conclusion. the net gain from increased mitigation drop off doesn't even come close to the net loss of having to face down the additional hull and shield regen rates of extra targets. do focus fire. its the best.
How important is it to have a balanced fleet? Is there a big need to have a balanced fleet when the AI is good, or when playing against other people?
try a Hard AI and see how well you do with just a single ship type. probably won't work very well.
all fleets need a backbone so you'll generally have more of 1 type of ship than any other, but support ships are vitally important at higher levels of play. there are generally three ships that are viable as backbones. the first is the Long Range Frigate. it does good damage against almost everything and is easy to build in large numbers early in the game. the second is the Carrier Cruiser. its expensive but very versatile and very hard to kill. fighter squadrons in particular are incredibly powerful, as i'm sure you've started to see. the third is the Heavy Cruiser. its a flying brick shithouse with guns strapped to the side. they're very hard to kill and do reasonably good damage to pretty much everything, although they have short range and can be outmaneuevered pretty easily.
in addition the backbone ships of your fleet you'll need support to enhance your abilities and protection to cover your weaknesses. Long Range Frigates are weak to fighter squadrons so benefit greatly from accompaniment by Flak Frigates, which are very good at killing fighters. Carriers are weak to Light Frigates so benefit greatly from accompaniment by some Long Range Frigates which are good at killing Lights. Heavy Cruisers are weak to bombers so they benefit greatly from escort by fighter squadrons which are good at killing bombers.
support cruisers like the Hoshiko Robotics and Cielo Command cruiser are very good additions to the fleet. even a small number of them will add a huge amount of capability. try it out and see. a small investment goes a long way. these are support ships so there's no point in massing dozens and dozens of them like you would with a backbone type ship, but adding a handful in with your main fleet will benefit you greatly.
Group Jump: It takes forever! Can't we fix this?
yeah, kind of a pain in the butt. taking off group move can get things moving along faster but it can also break up your fleet cohesion and risk taking losses as you jump into a hostile grav well. generally you'll have to manually go find the ships that are having pathfinding AI problems and give them new orders or else they'll keep ramming into another ship or some obstacle thats preventing them from forming up properly for the jump.
best piece of advice i can give to prevent the pathing AI from borking is to set your fleet group cohesion to loose. this will space the ships farther apart which reduces the chance they'll bump into each other. you may want to bring the cohesion back to normal or tight during combat though if you've got some reason to ball up (and there are lots of reasons to fight in a tight ball formation, depends on whats in your fleet).