What determines the ETA on system destruction, is it some sort of dice roll? Taking a beacon out into one of the Nomad system's exit wormholes seems to cause system destruction, but not without WILD variation in ETA. I've had anywhere from less than a minute, to more than ten before a system gets whacked. So, what determines how long it takes?
When the Beacon is deployed to a non-Nomad system, all Nomads move towards that system at a constant rate. It's kind of hard to describe - just watch the Galaxy map, and you'll see it happen. The detonation occurs whenever a Nomad system gets close enough (which roughly means, both system's star icons overlap).
If you are using an alternate view of the Galaxy Map, where the system locations are different than the default map, things get... weird. I suggest switching back to the default map when using Nomads.
One other thing, if I'm on a map which has no major branches as viable targets (meaning I can really only knock out small 1 or 2 system dead-ends), should I just deploy the beacon where-ever just so the Nomad stops being a threat to my planned defenses?
I wouldn't recommend using the Beacon to destroy anything but an AI Homeworld, or other equally essential target. AIP costs for blowing up that much stuff is very painful, and the time and effort involved in getting the Beacon activated, located, etc, is better spent elsewhere if you aren't using it against something really important.
Also, only the one Nomad that first arrives at the Beacon goes BOOM. If you have more than one Nomad system in the game, all others will resume their normal wandering after the Beacon is destroyed.
I don't know whether its worth the risk or not. If I clear the system of AI, but don't fully capture it, is the AI smart enough to move a large garrison fleet into it when its connected to AI system, and then wait for it to re-align to mine before unloading the garrison?
If you clear a system of all Guardposts but not the AI Command Station (this is usually referred to as "neutering") then the system will slowly reinforce itself, potentially building up a bunch of AI ships if it remains on alert for an extended time. Either a beachhead of turrets or regular sweeps of your fleet is recommended to keep a system like this clear.
If you destroy the AI Command Station, but do not yourself capture the system, the AI will no longer reinforce that system. AI ships will route through it on their way to somewhere else, but they will not deliberately garrison or defend it.