Questions on supply curve

I need advice on whether on my supply logic is correct.

Question 1: Any point on the supply curve indicates the minimum price that a producer must receive in order to supply a specific quantity of output. True or false?

I think, it is true because, if the price increases the quantity supplied would be differ. Thus, it is indeed the minimum price.

Question2: An increase in price results in an increase in supply but not an increase in the quantity supplied.

I think, it is false because price causes a movement along the supply curve. However, if the price of complementary good-in-production increase, the supply will increase, but this will also lead to an increase in quantity supplied, unless the demand decreases due to other factors.