Access my entire browsing history via Javascript
In general history is protected by the browser against javascript accessing it except through back and forward functionality. There are some hacks that can view some amount of history, but they are just that--hacks.
If you want to view/modify history programatically, you could do so via browser plugins. For example, Chrome plugins can use this API
EDIT
Mozilla also has some info about history modification available to Javascript here.
It also looks like this question talks about some of the same things you need.
Javascript only offers basic calls once your page takes control of the browser like:
history.length
window.history.back()
history.forward()
window.history.go(-3)
But if you were to write your own browser then you'd be using a 3GL in which case you'd be in total control of what the user has typed in the search or address fields you provided so you shouldn't have any problems there keeping a record of what the user did if you know what you're doing.