There is no limit to how tall the actual header can be. However, images that are placed inside of a header have a pixel limit of 300-pixels tall. The width of the header is limited by the max width of a form (since they are the same width), and the maximum width that a form can be is 1500 pixels wide.
As for the minimum height and width, those are defined more by the margins and the font sizes you choose (if you choose text). For width, forms have a minimum width limitation of 300 pixels wide. For the height, the effectual minimum height is 50 pixels tall, but an image or a font larger than the minimum would increase that minimum.
I'm curious to know if you have needs beyond those limitations and what the use case is. Do you need to insert an image in the header to be greater than 300 pixels tall?