Well they continue to grow regardless of the weather but when it is sunny they will put on more growth, especially vegetables.

Yes - but those that do best in full sun will grow better in sun.

They will still grow, but much much slower. Years ago I planted two cherry trees of the same type at the same time. I planted one in my front garden wich is directly north facing and the other one in the back facing south. The diameter of the trunk of the one in my back garden is about 3 times bigger than the one in the front. I expected some difference in growth, but it was a big surprise at how much difference it was.