If I have a program installed on a hard drive, can I put in a different computer and run it if both are on windows?

most programs have to be installed ... that is have entries made in the registry.

if, on computer A, the registry [and thus windows] is in the same drive as the program, then when you move the HDD to computer B, the program will be fine but windows will refuse to run ... you'll get the call microsoft window [because windows detected that it is now on a different computer].

on the other hand, if the program is on a hard drive that is not the one with the registry [is not the windows drive], then when you move that hard drive to computer B, the program will not run because it hasn't been installed to the registry there. it has to be reinstalled despite that it is physically present.

only the smallest of programs which do not require being installed will work as i think you want this one to .. run from non-windows hard drive in both machines simply by moving the HDD from one to the other

Depends, which program?

Unlikely.

Not likely- the registry and hardware drivers will be different.