You don't need software to unzip designs - just double click on the zip file. You do need software to put files into a zip file. 7-zip is free and will also extract the files from a zip file into a new folder with one click. You can do that without special software, but it does need some copying and pasting so takes longer.
yes, winzip or 7-zip. I am sure the new windows has a extracting program also. Find the compressed folder in windows explorer and right click on it to see your options.