I have downloaded Photoshop Element and when I go to my download section on my computer and click to open it, it opens something that is called WinZip. It is telling me that I have to buy this WinZip in order to run the photoshop that I just purchase

you should download two files. a 7z and an exe.  put both in the same directory and double click the exe.

Downloadable installation files available:

• Suites and Programs:  CC 2014 | CC | CS6 | CS5.5 | CS5 | CS4, CS4 Web Standard | CS3
• Acrobat:  DC, XI, X | 9,8 | 9 standard
• Premiere Elements:  13 | 12 | 11, 10 | 9, 8, 7 win | 8 mac | 7 mac
• Photoshop Elements:  13 |12 | 11, 10 | 9,8,7 win | 8 mac | 7 mac
• Lightroom:  6| 5.7.1| 5 | 4 | 3
• Captivate:  8 | 7 | 6 | 5.5, 5 | 1
• Contribute:  CS5 | CS4, CS3 | 3,2
• FrameMaker:  12, 11, 10, 9, 8, 7.2

Download and installation help for Adobe links

Download and installation help for Prodesigntools links are listed on most linked pages.  They are critical; especially steps 1, 2 and 3.  If you click a link that does not have those steps listed, open a second window using the Lightroom 3 link to see those 'Important Instructions'.