First question-yes.

Light frigates are a hard counter to carriers, support cruisers, and (i've heard) flak. make use of their antimatter draining abilities against carriers and support cruisers.

Start wtih the mothership, it gives you cheap upgrades. build a few disciples and try to take surrounding asteroids first, maybe also volcanic and ice planets when your MS levels up. prioritize its colonize ability, followed by shield restore.(late game additional progenitors can go malice/shield restore).

Yes. the mines act like fighters until deployed. except they never have any guns. once they are deployed, the carrier is free to rebuild another squadron(or switch to a different squadron type).

1. yes.

2. the mines. they don't have guns like other SC.

they act like other SC in terms of moving & docking & such. they do not attack except by laying theirselves(and that involves moneyz and a 30 second activation time during which they are vulnerable).

the best attributes of Light Frigates are the following:

1) they are relatively cheap, require no initial research, and no crystal at all to build.

2) they are very fast and can quickly chase down enemy units. 

3) they are extremely effective against support cruisers. they are effective defenders against siege frigates. they are the second best ships at destroying carriers (Heavy Cruisers are the best at this). 

the negative attributes of Light frigates are the following:

1) somewhat fragile. they don't stand up particularly well to anything. they are especially vulnerable Long Range frigates (Javelis, Assailant, Illuminator) which will wipe out large numbers of them extremely quickly. 

2) short range. this means that in order to gain firing position on enemy units they will often go out of range of your supporting abilities from capital ships and cruisers. they can be isolated in enemy backlines and highly vulnerable.

3) they use the worst weapon system of their faction (lasers, lasers, and pulse guns, respectively) and thus are somewhat less likely to benefit from weapon upgrade research. 

repulsion doesn't interrupt phase jumps.

Light Frigates become marginally more useful once they gain their anti-support ship abilities. The Cobalt removes AM, the Disciple actually steals it, and the Skirmisher doubles ability AM cost and ability cooldown time.

Even with these upgrades, their average lifetime in a fleet-to-fleet engagement is relatively short (although they have no particular weakness to fighters nor bombers).

Just played a game against a guy who was massing carriers then running around the planet with them.  Light Frigates OWN carriers so hard.  Oh god it was hilarious, he was trying to chase the carriers and my LF's with a bunch of heavies.

If he stopped the carriers my heavies would catch up and start destroying them, so he couldn't stop and let his guys catch up and couldn't kill the LF's due to flaks taking out fighters.  He ended up losing about 3/4ths of the carriers in this half-hour battle while we both constantly tried to reinforce our fleet.  Eventually he quit, as my ally had destroyed his enemy.

Anyway, moral of the story is, LF own carriers and people should use them more to take out carrier spam.

...its not so much that people think carriers own LF. its more like alot of people know that a modest escort of LRFs is enough to almost completely immunize your carriers from harrassment by LFs. the situation is usually that the mixed fleet of carriers + lrfs tends to beat the mixed fleet of lights+flaks. 

The solution is just not to run the carriers away from the cover of your LRF.  Sure, you lose some, but carriers are pretty tough so you won't lose many, and most importantly those strike craft don't die for a long time after their host is destroyed.  If the enemy lacks a strong fighter or flak presence, destroying a carrier might not have any impact on the outcome of a quick battle.

Light frigates are part of a mature and balanced strategy.  On their own, they'll beat massed carriers, but a modest addition of LRF will quickly put an end to that very quickly.  I bring my light frigates out later on after I have some LRF, carrier, and support cruisers of my own.  If my enemy is quick-teching to carriers then that's another story, but for a general-purpose strategy I find it's just too risky to build any considerable amount of them early on.  You just make yourself vulnerable to a LRF rush. 

if you want to learn how to win battles with good micro the first thing you need to learn how to do is mind your light frigs. if they charge into an enemy battleball they get gibbed by LRFs, period. you really just can't even start to kill their carriers with your Lights until you've taken out their LRFs with your fighters.

this is really the reason why most players find it to be a good strategy to really stock up on fighters. they're the most important unit involved for winning stage 1 of big fleet battles.

if both players are using mixed fleets that contain all 4 basic ships (carriers, lights, LRFs, and flaks) than the battle is likely to be settled not by who counters whom, but just by external factors like economic and technological factors and reinforcements.

the real role of heavy cruisers is that they are the only ship that breaks the symmetry of mixed fleets. they are nearly immune to fighters and flaks and take only light damage from LRFs and Lights. they deal moderate damage to lights and flaks but seriously pound the snot out of Carriers and LRFs. their only real weakness is to bomber squadrons, which is why once you've transitioned from mixed fleet to Heavies what you mostly worry about is providing fighter escort for your heavies to protect them from bombers.

I often build limited quantity of Model T cobalts to help with my early expension.  Many practices which have for long been discarted as "noob" and waste of credits are makign a comeback in the age of QuickStart.

Reason why light frigates are easily coutnerable is that otherwise you could pull off the most mindless spam in the world.  Thou I must say I am not that innocent, I have killed people with disciple spams before, even while they get fed!  Oh the joys of well orchestrated coups.