Applications should be installed in the root /Applications folder by default. This would not cause the "executable" to become corrupt when used by mutliple users, . However if you want to install an application so that only one user can use it, said application should be installed under /Users/myuser/Applications
Sometimes during install you can chose where an application will be installed, other times installers will default to the /Applications
Note that there will be some applications that require that they be installed in /Applications and will not function properly if they are moved into other folders or sub folders.
Apple mandates that ~/Applications and /Applications be equivalent for the function of apps, but not all of them obey the rules or potentially are aware of them. Same with user folders being stored on another volume than the OS - that's supposed to be fully supported, but sometimes it isn't.