I have a mid size lamp shade, can I just spray glue it and put cotton

Probably, but you can't just lay a straight piece of cloth on a curved surface. I would worry that a spray glue might be flammable even after drying; maybe a Mod Podge type glue would be less flammable. Take a large piece of scrap paper (several sheets of newspaper taped together, make a pencil mark on your shade for the beginning, roll it across the newspaper and trace the top and bottom to get your curved pattern until you get back to your starting line. Add at least 1/2" to the end for an overlap seam. Cut your pattern out and do a test fit. Should you add 1/2" to top and bottom for a foldover the wire rim? Are you going to add a finished cord or trim to cover the edges? This is why lampshades are so darned expensive in the first place! Another plan B is to make a tube of material a bit wider than the height of your shade with casing hems on top and bottom, run string through the casings, put it over your lampshade, pull to tighten, readjust the fullness, and tie the strings tight.

yes, but dry fit it first...make sure all the pieces fit nicely

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Yes. If you cut the material a little too tall, trim it with sharp scissors, then glue lace or another trim over the edges. If you cut it a little short, use wider lace, or rows of twine, or something else complementary.

You can use regular acrylic paint to paint the lampshade. Craft paint and even house paint.