[Kobal2]

Yes, PD appears immediately as you buy it. More buying, more units, effective immediately. You cannot see it outside of battle (the manual tells you what nations gets what units though), nor can you take units from it or move it around or get your money back in any way. MA Tien Chi also gains points of PD overtime as a side effect of its dominion, but it's a really marginal increase.

The PD soldiers replenish automatically to full at the end of the battle if you win it.

Not sure what you're talking about re: "a few odd units that I don't recall building", but it's not PD. Some commanders automatically generate troops around them though - for example, the Celestial General creates human soldiers wherever he goes, the Vampire Queen summons vampires once in a blue moon etc... It's usually mentioned in the unit's flavour text.