1) Как я могу определить URL предыдущей страницы, по которой я зашел на текущую страницу
window.document.referrer
вернуть URL-адрес, с которого открылась страница.
для двух других вопросов, вот пример из MDN :
Example
Suppose http://mozilla.org/foo.html executes the following JavaScript:
var stateObj = { foo: "bar" };
history.pushState(stateObj, "page 2", "bar.html");
This will cause the URL bar to display http://mozilla.org/bar.html, but won't cause the browser to load bar.html or even check that bar.html exists.
Suppose now that the user now navigates to http://google.com, then clicks back. At this point, the URL bar will display http://mozilla.org/bar.html, and the page will get a popstate event whose state object contains a copy of stateObj. The page itself will look like foo.html, although the page might modify its contents during the popstate event.
If we click back again, the URL will change to http://mozilla.org/foo.html, and the document will get another popstate event, this time with a null state object. Here too, going back doesn't change the document's contents from what they were in the previous step, although the document might update its contents manually upon receiving the popstate event.