1. It is quite possible for a ship to not need fuel. Our submarines don't, they use nuclear power. The ships could simply use a nuclear reactor, whic would explain why they explode so brilliantly.
4. Ammo, the plasma and lasers would not need any ammo, again they would use energy from the nuclear reactor, the bullets (if those Are bullets) would. However, those ships Are Very large (look at the size of the windows!) they could probebly carry enough for hours. Other, more crazy solutions, are portals to a world, teleporters to a world, or some sort of mass compresser that makes each material much denser, and when time to shoot, expands them and puts them together.
Nuclear powered anything still requires "fuel"...granted, it might last decades or centuries if only used for propulsion, but add weapons in the mix and you probably are going to need more uranium/plutoniun/thorium (or whatever you use to get your energy) every once in a while...
Honestly, I think it is conceivable that at least larger ships would have the ability to manufacture their own bullets and non-nuclear missiles given the raw resources...of course, whether they need to resupply for bullets or for raw resources, they still have to resupply...
Plasma does have "ammo" in that you need actual matter (plasma)...again, I think it would be unreasonable to convert raw energy into mass, so plasma weapons are still going to have to be restocked....maybe not in "bullets" per se, but in actual gas used to generate the plasma...
Lasers/beams are really the only weapons you could argue not having any ammo restrictions...however, they still need energy, which still needs to come from somewhere...call it fuel, call it the "reactor", call it whatever you want, it won't last forever...furthermore, high energy anything is going to probably needs lots of coolant and/or replacement parts...
With any of these weapons, a ship ultimately is going to be limited by something...once the ship's supplies are good enough for several decades, though, I don't think it hardly matters...I mean seriously, if you don't have the opportunity to resupply after several decades then you might as well just quit and give up on the whole interstellar travel thing...