https://www.sinsofasolarempire.wikia.com/wiki/Research_Trees is all I know of or you can try the forum search 

Volatile Nanites cannot be improved.  Once you've added one point to it, it's maxed out.  It increases the damage taken by affected targets (everything in a medium radius around the main target) and causes them to explode on death, dealing additional damage to enemies.  This can rack up a lot of damage.

As I've said before, I'm not sure what this does, but there is no noticable in-game effect.  It probably increases acceleration rate, but as I said it's not significant.

Yeah, they stack.  Absolutely scary damage when maxed out.

Some abilities are really finicky and require you to line up perfectly with the target.  This makes them impractical against moving foes, unless you manage to align yourself perfectly with them, which is tough in the case of the Jarrasul since it's a slower capital ship.  That's a hold-over from previous versions when it was way stronger than any other Vasari capital ship; these days that slow speed really gimps it.

If you have any other questions, ask away.

Volatile Nanites do not reduce their damage; it increases the damage they receive from your attacks.  You can always reference this thread for capital ship abilities:

https://forums.sinsofasolarempire.com/335807

It increases the damage they suffer 30%.

I'm actually not 100% sure of the value.  What I do know is that it's mostly used for its annoying effect on the targeting AI rather than for damage reduction.  When activated, any unit ordered to attack the structure will pick a new target, usually moving to attack something else.  This requires manual control by the opponent to override and actually destroy the structures efficiently.  In terms of damage reduction, it's far less than the passive bonus offered by the Advent Hanger's shield bestowal.

Yup, and not all costs apply to enslaved labour, either.  Research, capital ship promotion, and planet upgrades are all exempt.  It's not terrible, and as your income pushes higher this upgrade improves further, but in general you can't afford this early on.  If your resource income is really high (such that you're selling to make credits meet) then it becomes a lot more sensible, since it helps you avoid using the black market. 

If you're playing without the expansion pack, then yes this is the case.  If you're playing with the expansion pack, this is only true if you have starbases on both sides of the wormhole with trade port module upgrades.

I'll need a screenshot.  I'm not following you here.

IIRC, Power Draining Nanites is an ability from the Nano Weapon Jammer. PDN will simultaneously increase weapon cooldown time and bombardment cooldown time for hostile forces within range of the Jammer. First level of PDN does 10%/15% (weapon cooldown penalty/bombardment penalty) but a Tier 6 Empire research subject can increase this to 20%/30% and maxing out at 30%/45%. Each upgrade level also increases the maximum number of affected targets per cast (can't pull the exact numbers off the top of my head).

For Distortion Field, the Subverter must be facing the target to start the cast. Once the cast is started though, it will complete, whether the target moves out of range or not. DF can be terminated early if the ship it is cast on is destroyed before the cast time ends, or by another disabling ability.

For your trade route, that will depend on which wormhole leads to which. For Vanilla Sins, all uncolonizable gravity wells are automatically considered when the game determines your longest trade route, but for Entrenchment/Diplomacy, only these wells which contain a Starbase with a trade port upgrade will be considered (this has the consequence of Magnetic Clouds never having a trade route go through it).

Voruk's Labrynth is quite a dispersed map - you may want to keep plenty of scouts running around. If you're Vasari, one way to keep permanent visibility of stars is to research both levels of Phasic Cloaking (I think its a Tier 4 Empire subject?), park a Jikara at a star, turn off all autocasts, and use Phasic Cloaking. If PC is maxed, it drains 2 AM/sec from the Navigator, but the star restores 2.5 AM/sec, so you can keep the scout there indefinitely as long as it is kept cloaked.