Scenario:
I have two questions:
A. In Step 4, does the Browser store or cache the SAML Response and/or SAML token?
B. If yes, what kind of things (attributes? timeouts? protocols?) prevent me from taking that stored SAML token. Then coping it over to another computer (with a new session) and using that token to Login to the same SP?
The answer is "sort of" re caching. In your scenario, the Response will be sent via POST to the Service Provider from the browser. So the browser can "cache" the POST data that contains the SAML Response. So, just like any other POST event in browsers, if the user were to use the back button enough times after logging into the SP to get back to the POST event, the POST data could be resent to the SP.
There are a few things that help keep the Response from being hijacked -