If it's a picture of the same picture then it's known as the Droste effect. But a more generic for this is just a recursive picture.
at your profile on your profile pic it says change hit browse and go into your pictures and click the one you want
yes ,you can just left click on the picture and you will see a list of options listed out for you and the sixteenth word is delete. When you click the delete button you will see a link about "Confirm...
There are a lot of software which can help you. The most famous are Photoshop, Corel Draw and so on.