Any difficulty level above "normal" cheats.  Against the unfair difficulty and higher, this is very noticable.  Even though you have the best economy, the AI's are still able to field a bigger and better fleet.

I can't speak too much for the mods, but I can say that you're probably leaning too heavily on civic technology.  Your empire of six planets is respectable, but not large enough for those techs to really pay off.  You'd probably be better off directly investing that money in your military power and using it to capture additional planets.

Secondly, you need to scout more.  The whole map should have been completely scouted by the 30-minute mark.  This is particularly important for Vasari since they can capture extractors in uncolonizable gravity wells with their scouts.  This is basically free money you're passing up by not sending your scouts out to these locations.

Finally, in a free-for-all scenario you need to split your fleet into multiple groups to protect your flanks.  Remember, your opponents also have enemies on their flanks, so all you need to do is stay on the defensive when outnumbered, and then strike when the enemy is vulnerable.  Opponents who try to keep one powerful "stack of doom" as the AI does tend to get overwhelmed when fighting on multiple fronts so you'll eventually get an opportunity.  Although phase stabilizers can be a good way to mobilize one big fleet to defend your entire empire, they are expensive and more useful for larger empires.

It's Entrenchment, though I wouldn't put it past the DS guys to further improve upon that behaviour.  You'll need to keep your scouts in play.  If the enemy shows up in force to secure the neutrals, let them have it.  You can always come back in five minutes once they've left.  In any case, this still doesn't excuse not having the map explored.

On larger maps like this, auto-explore on its own does not work.  The auto-explore AI has certain inefficient behaviour quirks that can be corrected with at least some manual scouting.  These quirks unfortunately get worse on larger maps, so on one of this size you cannot rely on auto-explore for the more distant areas in the solar system.

You should probably have a pack of scouts (4-6) roaming about.  This is enough scouts that they can gang up and kill an unguarded colony frigate.  You can always come back later when the enemy gets around to retaking the extractors.  It's an ongoing thing, but Vasari need to keep coming back and hounding the enemy.

That's certainly one way to do it.  Your problem is that you're getting too many civic techs; a couple on the side isn't a bad thing, but too many can leave you without money for more important pursuits.  Early on, that's primarily the task of acquiring planets.

I haven't actually done a breakdown on scavenging, but unless you're destroying enemy structures on a very regular basis I'd avoid it early on.  The problem with this tech is that it's rather expensive to research, and at the same time requires you to be actively fighting the enemy and destroying structures.

As far as Enslaved Labour goes, some people swear by this tech, others are more reserved.  I'm in the reserved category; it's a great tech whose savings can add up, but that's a steep cost to pay in the early game.  It's definitely a worthwhile tech if you have the time and money on hand to go for it, but I wouldn't pursue it at the cost of my military or empire.