Cleaning up a picture on the pixel level

I am not entirely sure that I understand what are you trying to do, but here are few pointers:

If you want to change colors of individual pixels, you can use the pencil tool. It changes color of touched pixels to the currently active color.

The brush tool may be a better choice if you want to affect more pixels at once.

And also the floodfill tool. This one changes color of the clicked pixels and all similar (you set the tolerance in the tool settings) pixels around the clicked one.

Thank you. Is there a way of decreasing the size of the pencil, etc.? Presently it is a circle and therefore it is not very practical to manipulate individual pixels. Also, is there an instructional manual that a neophyte like me can use. Trying to procure instructions from the Internet is somewhat cumbersome.

Yes, there is a Drawing Tool configuration panel in the right column (you may need to drag it up or down, but it should automatically scroll into view, when you switch tool). There you can change the properties of the pencil or brush.

There is no centralized manual that would explain all features, but there are descriptions of tools and tutorial videos - look for the ones with Image or Photo tag.