Here are a few ideas/points:
1) As far as not seeing the missiles, its because you probably don't have an active resolution 1 active sensor in the vicinity of your fighters. Just because your larger unit can see the enemies some times leads you to think you will see the missiles. As it stands now, you are basically seeing them on your strength 1 thermals just before impact and don't have any ability to use point defense.
2) Consider making 250 ton fighter designs where possible. They are like 4-5 times harder to detect, so the enemy fire controls won't even be able to acquire you before you can fire missiles.
3) Consider adding some guass cannon point defense to all your ships. The lasers are good, but heavy. Myself, I like to make tiny 17% Guass Cannon turrets and just throw a few on every military ship I build. It might seem like a 17% turret will never hit, but with fast tracking, missile tracking, crew bonus etc they will have a reason % to hit. The trade off is basically like having one shot at 100% vs something like 10 shots at 30% for the same weight (those probably aren't exact figures, but I think you get the drtift)
4) For your carrier, I like 20-30% tonnage into hangars. You are high, which means your carrier is more of a fighter barge than a warship (which is OK if that's what you want). The big difference being rearming. With 136 magazine space, you can carry 10 of your size 14 torpedoes. You'll probably find having less fighters with multiple sorties will be a lot more valuable. I would add point defense too. You can easily get away with an 18 month deployment time, 1.5-2 year maintenance life and ~35B fuel so you can free up a lot of space there.
5) You're fighters are very well designed for your engine level. As mentioned, I use small 250 ton fighters when I can. I would suggest you consider a rail gun fighter in place of the laser, and add a tiny res 1 active sensor will also allow for the beam fighters to do their own point defense, even when isolated. I would also look at adding a thermal sensor to the recon fighter.
6) For the cruiser, it will work with 1/3 less fuel. If the idea is to use it for point defense, then I would get rid of the big turret and replace it with as many 10cm rail guns and small guass cannon turrets as you can handle. Think wall of lead. The current ship just doesn't have enough shots to splash more than 1-2 missiles per salvo.
7) I would pull a lot of fuel from your recon frigate. The passive EM sensor strength is probably a lot higher than you need. If you can research a bigger thermal sensor then consider that.
For transit operations, I normally build complimentary "scout designs" with the same tonnage as my other ships. Normally the small boys are jump destroyers and jump destroyers. Most of my designs have very light armament but the best passives I can spare. To jump your carrier, you may want to build a jump capable collier, as I find that the jump dive space penalty just too much to make an effective capital ship that can stand up to fire.
9) Also, consider using the same exact engine size to tonnage ratio for your whole fleet. That will give them all the same speed. As it stands now, when your fleet operates together, many ships actually have engines that aren't completely used, which essentially means you are packing less weapons, ammo, armor, etc than you could otherwise pack. Obviously fighters don't follow this and I do make some specialty frigates and destroyers that are over engined so they can chase stuff down.