Fairly obviously, you have to run the Audacity installer as an administrator.
Also Audacity will default to opening and saving files in its installation directory. If that is Program Files or Program Files (x86) you must change the directory to your own user space when saving files, unless you are already logged in as administrator.
To try to fix the launch problem I would open File Explorer, type:
%APPDATA%
hit ENTER on your computer keyboard, then delete the “Audacity” folder that you see.
Then run the Audacity installer again as administrator.