Repurposing Visual Metaphors can be confusing
People typically follow habits. If something doesn't work as intended, then it can confuse them or pull them off-track.
Web browsers (with the exception of IE in Windows 8 on a desktop) usually offer an intuitive method of backward navigation. Most of that navigation is pretty consistent between browsers by design. There is no need to reproduce that navigation in-page because you're taking up valuable screen real estate.
If you're designing a web app that works in app mode (mobile devices), typically back is on the left for English and forward is on the right. Most Asian languages in my experience work this way too because their interfaces are largely "Americanized" even though they may read from right to left or down the page. App mode allows the browser to act as a standalone app without providing the standard browser buttons. Designing a standalone app the interface should handle any navigation desired and be highly tested.
If you use "cookie trail" or "bread crumb trail" style navigation
home > category > page you should not include a back button in that lock-up for two reasons.
- If you use a real back button, then the people will return to the referring page (might not be on your site, so it needs to account for the referral).
- Most people expect the cookie trail to show the hierarchy of the pages. If the site has complex unrelated content then this can be useless.
Additionally most input devices provide a physical back button by design (mice, keyboards, track balls, tablets, and multi-touch pads).
For changing their results I would make the button say something to the effect of Edit or Revise this information intuitively near the content being edited. On larger screens if the interface is scalable then the back button may not indicate the ability to edit. Also some websites do not keep user input when people use the browser's back button by design. By making the previous page expire this causes the information to not be stored in the browser's cache (like using the back button on a banking site).
If you're not dealing with sensitive information I would make the site work in both ways so that they can "edit" and use the built-in navigation for their browser or input device.