Can I install the downloaded 32 bit packages to 64 bit OS?
(now using UBUNTU 12.04(32bit) and going to install UBUNTU 12.04(64bit) on another PC.)
Yes, you can. See this question for more detailed instructions, but basically:
Sometimes, the package will take care of the dependencies itself (particularly if you're getting it from a PPA) and all you need is for the partner repositories to be enabled.
Note: Most programs these days are available in 64-bit versions. If the program you're looking to install has one available, you should favor it over the 32-bit version, unless there are any known issues that technologically prevent you from using it (ie - it crashes on startup). 64-bit software is better equipped to leverage your hardware than 32-bit is, making it more efficient overall (and potentially allows the developers to add in features that weren't possible in the 32-bit version).