Record vistor history
 

I have a store at www.zazzle.com and i have a domain at www.hostmonster.com Zazzle host the website and i redirect my domain to it. my question is can i record events that happen on my store at www.zazzle.com if I do not host the content of the website. Also, if i did host the content, how could I record what a vistor did on my website without them knowing??

Use google analytics.

Will i be able to record data that gets imputed to the website. For example, if someone created a account with zazzle.com to buy one of my products will i be able to see there name, user id, and password? If not than can Google analytic do that at all?? If i hosted my own website can i use google analytics to record user input data?

no you can't.
if you host a website you don't have to record anything, since all data is being sent to YOU anyways.
if you you are trying to use one domain just to redirect users to other site and intercept data, then it is highly illegal and noone will help you with that on public forum (i hope)

Google Analytic is best tool to record all type of traffic search.