I'm wondering why you used the 32 bit version if your system is 64 bit?
One version is no less complicated than the other, the 64 Bit version would have run smoother and faster.
Downloading software is just the same as it is in Win 7 but it's easier to use the Distro's software manager/repository.
I don't know Zorin so I suggest you consult Zorin's Help manual and look for 'downloading and installing software' or similar.
As I said - reading required
btw, we now have a gazillion threads on the same subject. It would be easier for you (and us) if you'd keep all Zorin install subects/questions in one thread.