I'm afraid you aren't going to like the answers very much 
I was hoping there would be an easy way to spilt the various frigate types into chunks (taking half of each type, for example), and then tell the selected ships to "make yourself part of fleet A." I tried to use the fleet summary view on the left-hand side, but it kept shifting to the "all ships at this star" view, and the frigate icons are tough to distinguish at those tiny sizes anyway.
I then tried to alt-select each type of frigate and manually move them into seperate piles within the grav well, so I could visually sort them and grab the ships I wanted, but even after I told them to "stop" and turned off auto-attack they would still start moving on their own after about 30 seconds, getting all jumbled up.
There isn't a quick and easy way to do this, unfortunately. One thing you can do, instead of relying on the grav well view that shows all ships, you can first group all of them into a single fleet, and expand its display on the empire tree. You can then select whichever ships you want, and create a new fleet with them. Since they'll no longer be part of the original fleet, they'll disappear from that display and you'll only have the remaining ships left. You can repeat this process until you have however many fleets you want. It's a bit slower because you have to manually select all the stacks, there's no quick way to select half/third/quarter/etc of the ships, but you never have to leave the empire tree at least.
As for moving around, the ships always go to their fleet leader. If you seperate the capitals that are going to be your fleet leaders, all the little sheep are going to flock to them so you'll have an easier time telling what belongs to what.
Finally, even once I had grabbed, say, half the heavy cruisers -- there didn't seem to be a way to say "join fleet A" directly. I had to select fleet A, and then the new additions, and then make sure I had the right cap leader highlighted, and then create a brand new fleet. It was a real pain, especially with all the fleets moving around within the grav well while I was trying to reorganize them.
Sort of to go along with the above, the best way would be if you selected all the ships right away and formed a new fleet. To add them without moving grav wells you basically have to do the fleet reforming.
Also, I noticed that I can assign the rally point of a given factory to a remote fleet, and ships will travel on their own and join the fleet once they are constructed. If I have a "production world" with several factories, however, is there a way to direct output in a balanced way to multiple fleets? I tried sending three hangers to one fleet and three to another, but if you queue up dozens of new frigates you never know whicch hanger will actually build a given ship.
Nope, not really. The way the rally points work is that they point to the fleet leader. However, once the rallied ship reaches the grav well of the fleet leader, there's no guarantee that it will join that specific fleet if there is more than one there. This seems to be a bit random, so the best way is to make sure you only have the one fleet there.
You can set rally points for individual factories, and they build straight from the queue. If you have 3 factories and queue 30 Cobalts, each factory will build 10. It's basic first-in-first-out. If you always queue a number of ships that can be divided by the number of factories, you'll always know that each factory will spit out the same number of ships.
I know these weren't the answers you were hoping for, but most of these issues have been discussed in considerable length, at least, so Ironclad knows some of these shortcomings 
