I'd like build the kivy application which will work on 64bit Windows (and if possible 32bit also).

Is it possible that one app will work on both platforms?
Can I use 32bit system to build 64bit app?

This is probably simple questions, but I've never write code for these systems.
A lot of windows software is still shipped as 32bit-only, because for some reason compat with obsolete 32bit-windows still matters.  Alternatively, 32 and 64bit builds are available.
If you write your source code properly (without any assumptions about being able to store a possibly-64bit type in an int), you can make 32 and 64bit builds from the same source.  I think this is really unlikely to be a problem for python!
Building 64bit software on a 32bit platform is no problem.  You'll only run into trouble if you have a complicated build system that builds some tools (which are part of what gets shipped, so you build them for the target instead of host), but also want to run those tools during the build.
Kivy - build 64bit application on 32bit Windows