When I take a Capital can I instantly buy units if I own an enemy city

I see sometimes I can, but is that, because I own a city of the enemies prior to taking the enemy Capital?

It depends if he used the reinforcements in the city prior to you capturing it or not. So say you take the city of lyon in france, and he left 2 out of 5 reinforcements unused, when you take paris youll be able to produce 2 units in lyon.

From my experience if I can't defend the city I would spam militia or infantry, to stop my enemy from regaining reinforcement.