1) No experienced player would lose a capital ship to such a small force, especially a carrier, which does not need to be close to an enemy to fight. You should always build repair early otherwise you lose some of the value of having a capital in the first place. Retreat your capital to repair it.
His Assailants will counter your Disciples. The AI will have the Disciples fire on the Skirmishers for the better damage modifier, you want them to fire on the Assailants because taking out one Assailant will remove more striking power than taking out one of the Skirmishers.
A level 3 Halcyon should defeat a L2 Skirantra handily and have strikecraft left over, as with its passive ability upgraded it has 6 squadrons to 3 (base), and even Scramble Bombers isn't very effective at only its first level. You don't mention how you both used your strikecraft?
2) Assailants with four levels of research... thats up to the third tier, where Illuminators can be built, get approximately +100% striking power, so fifty hit like 100. You might lose firepower if you do not ensure your Illuminators are mixed up with the enemy, or 'shaking' to fire side beams. Flak would survive longer than Illuminators, and hit harder. However, see also the next point...
3) This sort of scale of forces just does not happen in games I play in. The 4v4 replay I just commented on, Warfleet was in the game for 48 mins and spent perhaps 75% of that time in full fleet combat. Capital ships are cycled in and out of the combat, as the number of frigates is kept far lower.
If I had to fight 250 Assailants and 50 Flak as Advent, for some unknown reason, I would know that I needed some kind of area weapon. Advent have such weapons on their starbase and their battleship, though a battleship would not survive long against that many frigates unless they are disabled... nor would a starbase The area effect weapon on the support cruisers is Repulse on the Guardian, which can be used to disperse enemy fleets. The Dominators are best used against single high-value targets.
Seven Halcyons cost a lot. You are outnumbered 2 to 1 in frigates and by far more in firepower. Having fewer capitals helps them level up.
Inexperienced players use fighters against LRF where the better counter is often flak. Not always.. a carrier capital can run rings around a grav well ( though carriers no longer can), but against numbers like those flak would be useful. Also, combined with Repulse your heavy fighter concentrations might work better. A sacrifice of one Guardian at a time is cheaper than one capital ship at a time. Your Illuminators could pick on an isolated portion of the enemy fleet.
With that many frigates even mines might work well, I'd have a go- though mines badly need more explosive power, they are area effect and 250 Assailants might pack into a small enough space to multiply their explosiveness somewhat.
