Fairly common in such a late game brawl.  The way to deal with this is to go on what's called a "rampage".  Build a couple Marza Dreadnaughts (spec them out with "raze planet") and a big fleet of carriers specced with bombers.  You will run past the enemy fleet, and attack planets and economic structures.  Use the bombers to quickly whittle away structures while your Marzas go to work on the planets.  Use your primary assault fleet to try and distract any defenders while you do this.

The goal is to cripple his economy and win by attrition.  If you succeed at this and move quickly enough, he will eventually be unable to replace his military units, and as soon as his fleet starts to shrink because he doesn't have the cash to replace it he'll simply collapse.  Alternately you could try building a massive fleet of carriers and try to vapourize his fleet with that.

The Marza has an ability called "Raze Planet" that deals massive bombard damage to planet.  It fires 2-6 rounds (depending on the level of the ability) that devastate the planet.  Siege frigates are terrible at bombarding in the middle of combat, so the Marza is TEC's answer.  If you want in-combat planet attacking capabilities, a pair of Marzas is your friend.  The Vasari equivalent is the Vulkoras, which is actually the deadliest planet bomber in the game (the Marza has better anti-frigate abilities, though).

If you don't want your Marza to do this, turn the ability off autocast and turn it back on when you want to bombard.  Turning off autocast is very important when you want to conserve antimatter.

Keeping your hoshikos close to your capital ships is a great idea.  That's done either by putting them in a fleet, or ordering them to stay together and switching them to local targeting (I prefer the latter solution since it gives me more leeway for micromanagement).  As for carriers, they are awesome late game additions since their strike craft have unmatched mobility and excellent firepower.  Bombers in particular are your best capital ship killers at this point in the game. 

No; gardas are only part of the solution, and even then aren't particularly effective against bombers.  You need a very comprehensive solution to deal with strike craft.  The Kol is a great addition in the late game with its flak burst ability, leaving all fighters and bombers in the area of effect seriously damaged (two bursts to kill if your Kol is a high enough level).  Of course, fighters give you the best overall damage output against enemy bombers, and are pretty good at against other fighters as well. 

These are great ways to deal with the strike craft, but really you're just dealing with the symptoms with any of these approaches.  The real disease is the carriers; you have to strike them down to deal with the problem once and for all.  The AI doesn't run its carriers away, so Kodiaks or Javelis are your best weapons for just smashing them with heavy damage.  Against a human player, expect to have to chase down those carriers, so the swifter Cobalt is useful in these circumstances (though if the enemy is guarding their carriers with real combat units, keep the Cobalts in reserve, since they drop like flies against LRF)

Fleets and assigning numbers to ships is part of advanced fleet control if you want. It is called microing.

Benefit is that it lets you select ships quicker.  I will give you an example. You build your first LRM frigate. Create a fleet with one ship in it and assign number to the fleet not ship. Now build carrier and do same thing but choose different number. So now you got 2 fleets each different type of ship in fleet. send them to different planet. Now on planet where you have factories set "exit point" on planet where your fleets are. If you build either LRMs or carrier they will go to the planet u selected exit point ant will join fleet with same ship type. So automatically if u press previous assigned number for LRMs all LRMs will be selected. Same thing goes for carriers. Now if you build any other ship type that previously didn't have fleet created (assigning numbers just speeds process of selecting-its not necessary) it will join strongest fleet in that gravity well.

Another part of microing is to tell ships what to do. And with bigger fleets and multiple types of ships it becomes hard to select same type of ships and assigning numbers becomes even more important. You can assign numbers to fighters or bombers as well. Each type of ship has counters (other type of ship that destroys it quicker and more effectively-there are some nice threads about counters) so its good if u attack right type of ship with their counter. For instance tell lrms to attack cobalts or cobalts to attack carriers bombers to attack heavy cruisers fighters to attack LRMs etc ets. In order to do that quickly you need those numbers assigned to ships. You can do same thing with empire tree its just slower....

And when you come to play online in MP games there are pros who can kill twice size fleet that they have or more with no problems with microing and nothing else. Another aspect of microing are abilities either on cap ships or frigates. By right clicking on them you can turn auto cast off and decide when you want to use that ability and in case of cap ships which one to use as well. Abilities cost Anti Matter and sometimes some other ability is draining ability you want to use but you cant because you got no AM.

There is science to microing and it takes time to learn and getting used to but benefits are great.  

Another thing for instance if you have 40-50  LRMs you can asign them to 2 diferent numbers. That way you are not wasting shots if you are attacking frigates since 20 LRMs will probably kill frigate you are attacking and other 30 that fired in this case would go to waste.   

PS you can assign numbers to factories as well. So u don't need to search for factory to select it. Press number and factory is selected. 

It cannot be deliverance engine (advent super weapon) because AI does not know how to build them. It has to be enemy culture from temple on nearby planet. You can see culture spread if you look at phase lanes. They become colored. If its same color you are playing culture is yours if not its players that has same color as phase line is.  

You definitely need to put some LRMs in your fleet. They are most versatile ships in terms that their damage multiplier is high to all types of armor. Each ship has its own armor type. Thats where counters come from. Its best to start with LRMs. Just build Cap that is for free another one if you want to, 2 mil labs research LRMs and build them straight away. Skip cobalts altogether unles you see AIs spamming carriers (light frigates are counter to carriers) LRMs are good at attacking capitals ships.  

Regarding flak.

Flak is useless unless you are against fighters or (this is manly for MP games online) you get sufficient numbers. They are counter to LRMs since they can fire at 4 targets at the same time providing enemy ships are all around them (microing). LRMs have slow turn rate and if flak circles around them they wont get attacked but they will fire at LRMs. 1vs1 LRM will kill flak no problem but 20 flak vs 25-30 LRMs flak will wins always with a little help of micro.

You can build your own culture center on planet you do own and wait till culture spreads so you can colonize or you can send cap ships to planet you want to colonize. Cap ships repel culture but if culture production on nearby planet is to strong it wont repel enough for you to colonize. Best choice is to use combo of the above. Build your own culture center and cap ships will speed up process of your culture spreading to that planet.

Thanks so much again guys...SUPER Helpful.

I was considering doing a bombing run w/Marzas and winning by destroying the economy. I will give some more attempts w/battles after reading the latest help.

Ah...you are correct. I did have the raze planet feature set to auto. I didn't realize that would over ride my initial command. Now this makes a lot of sense. Thanks for that one!

Oh I didn't realize you could number the factories! So helpful, nor did I know you could control individual fighter and bomber squarons. I thought the planes launched by the carriers were controlled via the carrier. That is, you click on the carrier and click on the enemy ship you want to destroy.

So if I understand you correctly, if I build one figher squadron and one bomber squadron from the same carrier, I can make each squadron attack a different target?

Yes

And not for TEC as much but for vasari mine layer or any other support  ships and advent repulse ..... If you have group and you pres TAB while group is selected you are selecting different ships oin that group to use abilities on. Otherwise you are using abilities just on first ship.

There is a problem with that because it doesn't work always..... Don't ask me why...... It has to do something with view (the angle and distance how you look on your ships...... I know...... ????????  

I noticed I could change my homeworld or capital planet...What are the advantages of doing this? And when/why would I want to do this? I assume it may have something to do with trade and communications, that is instilling allegiance into planets that are far away. Example, if my home planet is at the bottom right far away, and I gain say 10 planets, it would be better if my home planet was in the center perhaps?

an allegiance shift is why moving your home planet is helpful yes, keeping it in the center of the empire evens out the allegiance factor

Normally it's not worth your time moving your homeworld unless your original HW was in a really bad position or gets conquered. 

It's also an option If your HW is destroyed.

If you have no HW your allegiance falls to 25% so in this case you need to build new one ASAP.

HW also gives you extra credits but this bonus is not same on all planets. Terran and desert give you 4 cps. Asteroid gives you only 2 (or 3 not sure here). I have no idea about ice and volcano planets.