Losing ships - I started Eldar because I hate losing ships as well. This is helped somewhat by an approach focussing on standoff ordnance, and this is where Eldar benefit significantly in terms of stopping power - you can't stop things reliably with Hunters (nor can you also pull them away).
Weapons systems: the Pulsar is 7/8 hits, i.e. 1.75 lances. On Lock On it goes to 1.734375 hits, that's 2.3125 locked on normal lances. In other words, two Hemlocks, locked on, hit harder than a Locking On Hades. Suicidal Hemlocks are lethal, and a squadron of 5-6 will handily knock out a cruiser or cripple a battleship. Bring the squadron back to its senses with a pair of torpedoes.
The Torpedo is a rerolled normal torpedo, which because of its near-immunity to turrets can be launched safely in twos. When two Eldar torpedoes hit an escort it probably blows up. This is not close to true for normal torpedoes - if 2 torpedoes from a Cobra hit a Sword it probably stops one with its turrets and the other kills with 1/3 chance. A pair of Eldar torpedoes kill a Sword with more like 75% chance. This is very effective against escorts of all kinds (whose shields make Hemlocks somewhat less effective, though a Locked On Hemlock squadron will still easily kill the best part of an escort squadron.) It's also the most efficient weapons system against Eldar (Aconite guns do more damage for cost, but Nightshades beat Aconites when you remember you get many more of the Nightshades to take hits.) and Necrons (Hemlocks are reliable for making them brace, but then the Hemlocks are not so damaging.)
The Weapons Battery is between 0% and 130% or so more effective than normal batteries. IN prows, for instance, make bad targets, as you might as well be firing normal batteries. Torpedoes are generally preferable, but of course they take a lot of special orders to keep firing.
All Nightshade fleets are effective, but you are very heavily reliant on command checks, and it's usually a good idea to pick up Void Stalkers when you can. You basically have three good ships - the Void Stalker, the Hemlock and the Nightshade - and two mediocre ones - the Eclipse and the Aurora.
You should not try to compete in ordnance fights with fighters vs enemy bombers - particularly not with Tau. You should have a healthy respect for enemy bombers, and try to prevent their doing too much VP damage by spreading hits out among your escort squadrons. A preferable approach is to inflict sufficient pain to disable the carriers. Instead of an Eclipse, for instance, you could take 6 Hemlocks. Tougher, and much better at promoting suffering. If they don't have their carriers in their front line their ability to bomb you into submission (or stop your torpedoes) goes down significantly.