If Apple OSX's Archive Utility cannot open it I'd be a little concerned. Just select the zip file, go to File menu, choose open with ... Archive Utility or what it's called for your version of OSX. Stuffit Expander is a 3rd party option of course.

As for downloading programs for OSX, try to find out what size the file should be first so you have an idea what size you should be looking for so can exclude spam or rubbish from your search results.
Searching .dmg under a program search can help to find mac specific program files.

Installing: Generally mac programs are on a dmg (disk image file) which should be opened thus mounted on desktop (open the disk image if the folder inside is not already opened). Then the installer file will be inside. Depends on program. Some are installers, some you simply drag and drop the program to your applications folder. There should be a Read Me file inside which explains about this. Most mac programs have support files built inside the program package itself, thus no installation necessary. Some programs require support files to be installed to the system folders.