The answer to the first question:
Open the Hypershader (Window>Rendering Editors>Hypershade), then create a new color (phong, blinn, lambert, whatever), then in the material attributes editor click on the checker box next to color. Choose File and then browse for your file. Then here is a small trick: Open the shader, click on the new color and choose graph network. Then delete the connection from the file to the color. Then click on the color, middle mouse button click the file and drag then let go over the final color. A menu will pop up asking how you want to connect it, choose connect to bump map. And toodaaa, there you have it, your file on a map.
I have a tutorial written to explain all that, im trying to get it posted but its so big i cant post it.
As for your second question: That is the UV texture editor (Window> UV texture editor). This is probably one of the hardest parts of Maya to me, so I cant explain it really well. But you need to unwrap your model and then you can export out an image from the UV texture editor, paint it, and return it back to the model.