We are in the transition zone, too hot in summer for cool season grass to perform well, too cold in winter for warm season grass to perform well. Do you know what kind of grass you have? I would stick with whatever you have and try to improve it with proper mowing, watering, and fertilizer. if you have a cool season grass like fescue, the bare areas can be overseeded in early September. As for the shade, it looks like grass is growing under the trees. You could mulch in circles around the trees and that could simplify mowing (and protect the trees from the mower). As for leaves, mulch mow them into the lawn in the fall. They are valuable organic matter and will help improve your soil. Just run your mower over them (might take a few passes to get them in small pieces) and leave them on the lawn. You can process lots and lots of leaves this way. Use your blower to get them from under the trees to out in the lawn and then mow them. The mulch, if you add mulch, should stay mostly in place when you blow the leaves.