Every faction can do this if the extract is in an uncolonizeable gravity well. The Vasari have it on their scouts, the others on their colony ships.

Expanding fast is the key early game. Build a mother ship and have it take a volcanic or ice by itself, while you send some frigates and a colony frigate to take asteroids or moons at the same time. Try to switch to Corvettes or Flak ASAP instead of Light Frigates.

Don't get trade too early. The fastest way to make money is to colonize planets and build the minimum population upgrades and extractors, and this sets you up for having more research labs and trade ports later.

Try to get the relationship upgrade techs as fast as possible, and try to figure out which one of your neighbors is most likely to attack you and destroy as much of their stuff as possible. Other players like people who blow up their enemies, so if you're just turtling or avoiding combat you might have a harder time making allies. Your first goal should be to get a trade treaty, as this will allow relations to slowly increase on their own (assuming you have trade ports). One thing to keep in mind that throws off new players is that you cannot arbitrarily decide how much you like a faction. Diplomacy is two way, so if one player is constantly blowing up your ships your people will probably hate them, preventing you from doing any sort of diplomacy with them.

As the Advent Rebels, you have decent Diplomatic options, especially with the TEC Loyalists or Vasari Rebels (plus yourself of course). The Vasari Loyalists don't particularly like you but its not impossible, but the TEC Rebels and Advent Loyalists will hate you quite a bit, so it will be very difficult if not impossible to make allies with these two factions.

Usually those ships have other intended roles, like siege frigates bombarding planets, colony ships colonizing planets, etc. As a result they are only slightly armed, and are not meant to engage with other ships at all.

I don't use formations or fleets in most occasions. Sometimes I'll setup a fleet next to a starbase and then set the factories to use that fleet as the rally point. The reason is units in a fleet will observe the engagement range of the fleet and you can't set the default engagement range out of a factory. This is useful when you want ships to stay near a starbase while your building more ships during an attack.

Otherwise I move units manually and set the engagement range based on the micro I want to do.

Always upgrade the first level of asteroids and dwarfs and first two levels of planets.

Look for planets that have maxed their current population but still have population upgrades such as dwarf, ice, terran and desert.

Trade ports with a long trade line generate the most income in the game. The trade line can be seen by hovering over the credits in the upper right of the hud.

Corvettes and Light Frigate to start. Then add units based on what your encountering. There's some good threads around that talk about units and their counters. After that learn how to use Guardians and Dominas. Both have great primary and secondary effects.

Advent likes synergies too with it's capital ships.  

Then Chastic Burst, Chastic Burst, Chastic Burst. If you can Wail an enemy, make sure your titan is there to get the instant Experience boost and then choose Chastic Burst.

You picked them as your favorite without knowing what they can do?

Their titan, bringing stuff back from the dead with return of the fallen and reanimation, and wail of the sacrafice. The before mentioned Chastic burst on the Eradica is devastating to large enemy fleets, use it as much as possible. Return of the fallen is fairly early tech and can be very economical in long games, but it doesn't have the same immediate impact of say getting repair bays because it spawns the ships at your homeworld. Reanimation on the other hand is much more direct and useful, as it lets you bring back an enemy ship you destroyed right at the battle site, basically allowing you to get temporary reinforcements for killing ship.

Finally, Wail of the Sacrificed is their truly devastating late game technique. It allows you to destroy one of your own planets with a culture center to inflict 20 points of damage per population that planet had to every enemy ship in adjacent gravity wells. Even a lowly Volcanic planet can inflict 1400 damage this way, easily killing corvettes and unmitigated LRF. An ice planet can give you 3200 damage, enough to guarantee a kill on anything smaller than a Heavy Cruiser or Carrier Cruiser, and if you happen to sacrifice a full population terran planet, that's at least 5600 damage (more if you have pop upgrades), enough to destroy everything but caps, starbases and titans.

The ability to instantly destroy an entire enemy fleet simultaneously and without warning can win the game if used right, but you must be careful when using it. Remember it doesn't do anything to the planet that actually got sacrificed, so good players will probably try to split up their fleets and send them in groups to the planet they think you have wail on. Unless you happen to get a great map set up where you have multiple higher population planets overlapping each other, its a very risky defense because of that and because after its used, it will take a long time for the population to regenerate after you recolonize it. It is often more useful on the offensive, as you can take a planet next to an enemy strong hold, wait for the population to build up, then wail it as your fleet jumps it to make it much easier to take.

IMHO, Wail of the Sacrificed is cheating (in PvP games) because it is so severely overpowered and contradicts what the game is about.

TEC starbase red button is a powerful ability too--but that can be avoided and it only affects a portion of a gravity well.  Some titans have overpowered abilities--but you can run away from them if necessary.  The Marza missile barrage is powerful--but you can run from the Marza or find a way to kill or disable it.

In contrast, Wail affects numerous entire gravity wells at one time and makes it essentially impossible to position a fleet such potentially affected gravity wells and to defend them.

I'm messing with the Advent myself. (though I'm liking the Loyalists more) For me, I usually capture several planets and try to build up defenses first...until at least I can build Starbases. And the way I set up my defenses, it makes it very hard for any fleet to take them out. (honestly I don't know if difficulty levels affect ship's attack power or not, usually play on Normal until I find my best faction) But a planet of mine invaded one of my planets with a full fleet and a level 10 titan. Lost only one beam platform, and my Starbase barely scratched, lol.

I would agree, normally.  But in a game with pirates, you get many more options.  

For instance, you could send the pirates after your neighbor at the same moment as using the wail and then attack him in another place, causing chaos and splitting his already weakened fleet.  Doing this can be very effective.

And dont forget the WotS/Malice combo.

QFT

Wail is very currently very powerful, but much of that power comes from the fact that many people dont know or forgot about it. In a recent game one of my allies managed to loose 4 large carrier fleets to it. I could understand it the first time, but afterwards we explained to him in detail of how it works... well he thought he could outsmart the other guy but this one was always vigilant and so he wailed him 3 more times. Our allys was no power in the game anymore because he could not rebuild his fleet in a timely manner after the 4th wail. But so he deserved for such foolishness.

WotS can swing the balance of power in team games. because it punishes people who overlook its danger. I recently had the following situation. All of my team knew that there was a gravity well that was a lethal outlet for wail. We all avoided it. But after a successful battle we regrouped and one of my team didnt realized his fleet was taking the shortest path.... right trough that lethal gravity well... an invitation that was of course accepted. With nearly a fourth of our fleet just gone the balance of power swang back and we finally were the ones that were defeated.

It is imperative to attack the origin of the wail after it has been used... there is never ever going to be a better time.

Wail can be a nasty surprise in larger FFA games... when you have 2 or more people coming down on you it is easy to forget or even to dont know that that planet above is now in firm AR hands. A single seeker vessel doesnt seems to be of much concern when you have 2 hostile fleets in the system. Well... shortly after there were 3 people who just lost most of their fleet, not to mention a very nasty XP boost for that Eradica.

I dont think you can use WotS as an offensive mean much... population grows quite slowly and if your enemy in all that time never scouts or never moves his fleet away... in all honestly he deserves every single lost ship.