Could download of open office harm my computer windows 7 64 bit. pop-up said it can
I wouldn't worry about it I've never had trouble with it. If your computer starts acting weird then I would do a system restore which you can learn about here: http://windows.microsoft.com/en-us/windows7/products/features/system-restore
Downloading Open Office should not be harmful in any way. Users often get the 'Download site is harmful' pop-up when opening an .exe file for the first time. Some .exe files can contain viruses.
If you get the download from an approved site...no problem. go to Mozilla to get it.