Can a block stretch edge to edge, or fill the whole screen?

Yes, and any block can do it. In the page editor, open a block's Config tab. Turn on Full Bleed to stretch the block edge to edge across the whole window, past the page margins (the block needs to be full width). Turn on Fill the screen and center to make it at least one full screen tall with its content centered. Both work together, which is how a big opening section is usually built.