My question is about subsidy contracts:
When can they be made? Can I create one, for example, at the moment I draw cards?
There are no restrictions on the timing of subsidy agreements. Of course once cards are drawn they can never be transferred between powers, so the agreement made would begin to take effect the next time the powers in question draw cards, which in your example is immediately.
Also I missed that only Major powers can create Subsidy contracts. Does that mean that the starting contract between Bavaria(-1) and France(+1) would normally not be allowed?
You've got the starting contract backwards- the first year France is drawing -1 card (because it is subsidizing Bavaria) and Bavaria is drawing +1 card.