ISboxer is always 32bit, there is no 64bit ISBoxer. Inner Space does have a 64bit version, but unless you choose specifically to run the 64 bit Inner Space, the default is 32 bit.
Any process that is launched from an admin process is running as admin. As Inner Space needs to be an admin process in the first place, and has code in it to request admin privileges, Inner Space is an admin process, thus anything Inner Space runs will also be an admin process. You should avoid setting the Application Compatibility flags, as this causes Windows to load the App Compatibility database into the running process and this can cause incompatibilities with Inner Space (which is just an oxymoron if I've ever heard one)
As for 32bit. If you have a 32 bit OS (or a 32bit CPU, which will then require a 32 bit OS) then you can't run a 64bit process. Unless you specifically point Inner Space at wow-64.exe, then it will use 32bit WOW and not try and launch 64bit WOW because the code in WOW that relaunches the 64bit version will detect that your OS and/or CPU is not 64 bit, and so not try to run a 64 bit process. Even if you pointed Inner Space at wow-64.exe, it would fail to run because you cannot run a 64bit process on a 32bit OS/CPU.
In all cases, your points are not correct. If you are having trouble launching a team then either your computer is not powerful enough or you have some other software which is incompatible. You should post a diagnostic
http://isboxer.com/wiki/Diagnostics.