You can only produce ships or troops in cities (700+ population)
Each province can only raise a certain amount of men, build a certain amount of ships, at one time.
Most likely, however, what you are referring to is a tax base problem. If the province has a city, but the shipyard and/or tent is darkened, it usually is an indication that you have an insufficient tax/population base. It's not just having the ducats in the treasury -- it's having a financial infrastructure to recruit and maintain the forces you raise. If your shipyard/recruiting tent is dark, place your cursor over it and wait -- a message should pop up explaining why.
Even the biggest, richest powers can only raise so many troops and build so many troops each year. At some point you excede that infrastructure, and you can't do any more.
Manpower and resources aren't infinite. Early on in the game, with underdeveloped economic bases and infrastructures, you can reach that limit pretty fast.
So build carefully.
You can never demand or receive more than three provinces from a foe in a normal peace treaty. The only way you can get more than three provinces from a single war is to conquer and annex the entire nation. To annex a nation, you have to hold every province. When you go to the peace screen, all the stars will be present and an "annex" option will appear at the bottom right. They may not agree to annexation at your first request. You can never annex the captial province of a major power.
