The law of supply and demand - How does it work?
You need to take into account the cost of producing a good as well. In most cases, the marginal cost of producing something is increasing. A profit-maximizing producer would want to produce until price is equal to marginal cost. That means that scenario 2 is responsible.

For the case of rising prices with no increase in demand, just think about the basic demand and supply model. What could cause an increase in equilibrium price without the demand's changing? (Hint: a shift in ____). What could cause that shift?