I had a suspicious install include the installation of 7zip. It put a link to 7zip on my desktop that executes the program SevenZip.exe -expose
Is that a legitimate program that comes with 7zip or is it a fake that I need to get rid of asap?
Original 7-Zip does not have a file named SevenZip.exe, so the software you have got is not 7-Zip. It may well be legitimate though (for example, it might be a clone of 7-Zip with similar capabilities), but in this case its installer should clearly state the difference. If it does not, then you would better uninstall your program and, perhaps, perform a full system scan with your antivirus.