CREATION
When I grab ships and select "fleet," half the time it puts the fleet leader as some insignificant ship instead of my cap ship. Then I have to do it over again, or keep fiddling with it until I get what I want, wasting precious time. What's the best way to create a fleet?
When you select your ships, use tab to quickly cycle through the selection to select the "main" ship. Its selection border will be much whiter than the others. Then hit create fleet.
SELECTION
When you own enough systems to scroll off the page, and when you double click your fleet icon at the top in order to jump to it and center on it, after the first click in the "double click" the systems scroll up, and you end up not jumping to / centering on your fleet, rather you end up clicking on some system you did not want to click on. What's the best way to grab a fleet and center on it when you have many star systems under your control, so double clicking the fleet icon at the top is out?
Space bar is the key to focus, not double click. So you can click once to select, and then space to focus on them. The key works for pretty much everything, even the event cards you get on the bottom 
JOINING
More than half the time ships do not auto-join my fleet. If my fleet is parked in the grav well where frigs are being built, when they pop out they do not auto-join. Sometimes they do not auto-join when I send the frigs to another system which contains a fleet. I know you have to right click auto-join - which one? The auto-join of the fleet (or fleet leader), the auto-join of the newly-built ships which you want to join a fleet, or both?
Most/all combat ships should have default auto-join on. The main thing is that they need to end their destination in the grav well with the fleet, else they will fly by and not join. You can also set the planet's rally point to the fleet leader (just use the fleet icon as the rally point target) and then all ships built by that planet will rally to wherever your fleet is and join it. Note that if you move your fleet around, they'll fly to where it was first when the ship popped out, and then they'll attempt to catch up from there - they can't dynamically adjust their waypoints.