Supply Ships?

Build a ship with alot of solar panels. When the ship fill its supply storage you can manually cargo transfer the supplies as needed.

Another way is to build a ship with alot of storage and a few emergency resupply pods. When the supplies run try, set off the pods and then distribute as necessary. This method needs a handy repair system nearby.

I haven't gotten far enough in a game to get quantum generators so I cannot give you any pointers there.

Note: ordinance can only come from a supply center on a planet, though I have made an ordinance ship using the ordinance supply storage and a few emergency re-ordinance thingie. Again you need access to repair.

Kerry-

"...I say we must move forward, not backward, upward, but forward, and always twirling, twirling, twirling towards freedom!"
-Kodos for President

well, if U create a fleet of your ships in the system, they will run out of supplies in about 3ish turns. You must create a ship, a supply ship, which has 1) either command, engines, and supply in it, 2) one that has either solar panels or a quantum reactor thingy. If you have a ratio of 3 normal ships for each one of these supply ships, (in a fleet) the supply ships automatically distribute the supplies.

my strategy is to use meson cannons, which do more damage than depleted uranium cannons, are smaller, and only need supplies 2 operate. Make your warships armed with meson cannons, and have EACH of your ships have about 1 quantum generator for frigate, destroyer and light cruiser, cruisers have 3, and battleships and Dreadnoughts(my favorite) have 5 quantum generators. That way, your ships almost never need resupply, unless their quantum generators get blown to heck in a battle.

To increase fleet endurance
1 research cargo to tl5+
2 put supply and ordinance modules on ships
3 build fleet support ships cruiser or light cruiser hulls with light defensive weapons shields and armour but lots of supply and ordinance modules one of these ships will be viable and hold 30k of each
4 use energy weapons primarily
5 use reactors or solar panels to supplement this
6 put emergency result or reordinace pods on ships & include a repair bay in the fleet with repairing these at a fairly high priority

Thats just cheating in my book, but it works so if you or anyone else wants to do it then go for it.

Six might be cheating and it’s not something I do but it is a way of increasing fleet endurance. I don’t use it as to be honest I don’t need to with supply ships and TL10 in cargo tech I don’t need to

To answer the first question, ships in fleets auto-share. A fleet of nothing but combat ships isn't going to get far, so plan some logistics ahead.

I think that supply still distributes among ships in a fleet, but I've not tested it.

Kerry-

"...I say we must move forward, not backward, upward, but forward, and always twirling, twirling, twirling towards freedom!"
-Kodos for President

I tend to build my frontline systems with laods of resupply depots, and when I have about 40k research points do a couple of turns on spaceship supply which makes my depots far more effective after they have upgraded. I tend to defend myside of warp gates as this means I don't have to worry about resupply beyond my depots, my invasion fleets have enough to grab and hold a planet then refresh by squadrons.