1) No, the physical location does not affect the productivity of the trade port. 

2) You should definitely leave the guardian shield ability on, but you should turn off autocast when you aren't in battle.  The guardian has a bad habit of wasting antimatter on this ability if an enemy scout flies by.  As for repulse, yeah, it's a little weird and I haven't fully figured it out myself. 

3) PJI's don't stop a fleet from phasing out, they simply increase the "charge up time" by 700%.  They will eventually be able to warp out.  Also keep in mind that PJI's don't affect the entire gravity well.  If the enemy moves far enough away, they can jump out of the gravity well without being affected by the PJI.

4) Population and fortification upgrades are two different things.  Don't confuse them.  Fortification upgrades do increase the hit points of your planets and make them take longer to destroy.  This is a great delay tool and is also useful against the AI, who likes to build lots of siege frigates (humans rarely do this in multiplayer).  The best reason to buy these is if your opponent has a level 6 Jerrasul Evacuator.  The "drain planet" ability deals 1350 damage to the target planet, leaving only a tiny amount of health if it's unupgraded.  Having at least one upgrade to survive this ability is important!

5) When it comes to a battle of attrition, flaks beat strike craft, end of story.  If you have a relatively equal economy to your opponent, you cannot beat a flak-based army with a carrier-based army in a straight fight.  You have a couple approaches here to deal with this situation.  The first is to play hit-and-run.  Flaks suck at wild goose chases, and strike craft excel at them.  However, this leaves you with few defensive options.  The other approach is to change your army makeup; heavy cruisers work very well, and if you have fighters to counter the enemy bombers, they're a great addition to your army.  In theory light frigates counter flak, but in practice long range frigates will annihilate your light frigates before you even scratch those flaks.

6) Add guardians to that mix and you have a winner.

7) I rarely build starbases as Advent.  They're too expensive and your money is much better served by building a bigger fleet.  A smart player will ignore or circumvent a starbase anyways.  Against the AI, mass disorientation and meteor control are excellent abilities, but a player will seldom give you the opportunity to use them.

8) Don't know.  It's annoyingly long, but I believe it's shortened if there's a frigate factory in the system (just based on my own experience, they seem to come back faster)

Illums+Guardians+Aerias+Defense+Holy Trinity=Good Fleet.  These ships are awesome.  Every single one of them is great at what they do.  

Illums are awesome.  They have great DPS if you know how to use them.  It takes microing to get them in position, but once using their side beams, they become a force to be reckoned with.  Oh, and don't forget deceptive illusion.  This essentially doubles DPS by making a second Illum (which has operational weapons btw.)

Guardians soak up damage and are practically mobile PJI's.

Aerias carry three squadrons (and most efficient FS of any carrier) and each squadron has a ton of SC in it.

Defense vessels have six turrets and good DPS.  Flak ships are also good at fighting LRF's.

Holy Trinity:

Progenitor: Should be your first cap every time (unless on Point Blank at which point it should be a radiance).  Malice is wonderful.  Despite its nerf, this ability is still good and can multiply the damage of side beams, Ruthlessness, CB, Vengeance, and many others.  Shield Restore is great for helping out your frigates.  that thing heals 400 shields on anything within its radius.  Keep your fleet in tight formation and this can heal almost all of them at once.  Colonize is also good.  The cost redux is great.

Radiance: Arguably the best direct combat ship in the game.  It has EAA which reduces damage and regens AM.  Wonderful passive.  Det AM is a great anti-cap attack.  Not quite as good as Nano, but it can stop the dreaded MB.  Animosity is good early game for keeping your illuminators alive and when used with a couple Dominas, SR, Vengeance, and Malice, this is not something to be scoffed at.  Top all that off with Cleansing Brilliance.  This is perhaps my favorite ability in the game.  If you want to kill a cap, use CB.  Nano is a death sentence, but CB is the guillotine.  Once you aim CB at a ship, you can feel safe that that ship won't be around much longer.  Combine this with Malice, and you are dealing 75 DPS (or more under certain conditions) to nearby foes.  CB rocks.

Halcyon: Great cap that you do need.  It neutralizes SC.  It takes the damage from FB and the AoE from JW and combines them.  Telekinetic Push is certainly the best anti-SC attack in the game.  Adept Drone Anima is kinda worthless until you get to higher levels at which point it is like adding two more squadrons to your ship.  Energy Aura is great though.  It buffs "all nearby friendly weapons."  In other words, this is a blanket damage buff for the Advent.  At its top level, it decreases cooldowns by 22% which translates into about an 8% increase in damage.  That is very respectable.  Anima Tempest is either loved or hated.  In the right hands, this ability can be used to wipe the enemy from the field of battle.  In the wrong hands, its a waste of 120 AM...  Simply put, this thing will double your SC counts at level 10.  This is a very good ability in my eyes.

Of course, all these things are worthless without a good player commanding them.  Use these ships wisely, and you can take on fleets 2-3 and sometimes ever 4 times your size.  A good advent player is a not something you want to face.  Although I love their synergies and capitals (I absolutely love the Radiance) I find that Vasari fit my playstyle more and as such, I don't use Advent much...  When I do though, I deeply enjoy it.

Hotkeys:

the 10 buttons on your keyboard between "q" and "g" represent the 10 buttons on your display.

The OMFGHS factor for Advent is when you come with your fleet. Advent's speciality is having the most badass fleet in the game, period. Forget the bullshit, just build your fleet and fly around taking out their infrastructure.

Uhh..  The HT is Prog (colony), Rad (battleship), and Halcy (carrier) and should be built in that order under most circustances.

For me, I dont scuttle the cap ship factory as Advent unless i know tha im not oing to build another. Instead Ill usually upgrade logistics fo extra slots. The reason why is that Cap ship factories are expensive and having to build another one + getting Cap supply + additional fleet supply often jst takes too damn long. With a Marza at lvl 5 or egg at lvl 6, I wanna be able to get a Revelation or Radiance fast.

Trade ports will start you earning money as soon as the first trade ship pops out, but wont max out for a few minutes. Killing enemy trade ships is supposed to earn you some extra scrap, but Im know its not really a great source of income, and Im not really sure how bad it hurts your opponent.

Unfortunately no, this game does lack a patrol behavior. The best thing I can say to do is give them a nice long list of things to do and check on them every so often. Also, 2 scout can take out the 1 siege frigte floating around asteroids, making it really easy to colonize these with jsut 2 scouts and a missionary vessel. Ill often do this after capturing neutrals with my colonizer to help expand.

Everyone uses fleets a litte differently based on how they like to play. Personally I'll only set up a fleet if I need new incoming ships to adopt a certain behavior like hold position, this way they don't go kamikaze after an enemy starbase/fleet/defenses as soon as they reach their rally point (usually my mothership). Otherwise I just use control groups for specific units like fighters, bombers guardians etc.

The others are right, Advents mid-late game strenght is in their (cap) ships and fleets. But you should also have your culture slowly raping your enemies border worlds.

Also as a general rule for early game, if your nearest opponent is Vasari, upgrade all your ships health to help cut down on ships being destroyed by phasic bypass. Against TEC or Advent though I usually upgrade shields first to increase the power of the motherships shield restore.