[Taz-in-Space]

If you have an experienced fleet and add an FNG - does that newbie acquire some of the experience absent a neural net? If so - how much?

AFAIK, there are TWO experience modifiers: Fleet and Ship. If you add a ship to a fleet it will get the fleet bonus automatically, but will not modify the Ship experience(without the Neural Net). I believe , but have not tested, that the neural net is required to add the best Ship experience.

Does it make sense to train up a fleet of 60% completed hulls to the max, refit and then distribute them to other fleets?

A fleet's experience doesn't follow a ship to another fleet. (but the Ship experience does.)

Start out by considering the question: How soon do you research Adv Military -> training facilities?

I usually wait until mid-game to add this. there are other things that I believe are more inportant. ECM SENSERS GOOD WEAPONS ARMOR SHIELDS PROPULSION ETC.

Can a TF be built on a orbiting base?

NO. But you may be able to MOD a component to include the training traits.

What about moth-balled ships in a system and/or sector?

Interesting question. I don't know, I never tried to train a mothballed ship.

Do Fleet/Ship/System TF's stack?

Yes. Take a planet with moons. add training facilities to planet and moons. note that training is now faster!