I am trying to remove a photo in my Moodle profile and add another one but it keeps reverting back to the first. How can I change this?

It is recommended that you give your new photo a different filename to the previous one. This should fix the problem.

You may also need to clear the History and the Cache in your web browser to see the changes on your computer.

How do I display an image in a Moodle wiki?

See attachment for instructions.

How can I add an image to my course page?

Images can be added to the page either in a label or in an HTML block.
See this guide for instructions.