Scroll top top
On my iOS device I can touch the menu bar at the top of any application to get to the top (where menus etc most often are). Many websites solves this using various home made solutions, most of them not really that good, but worse it they never behave the same. This could easily be solved by the web browser manufacturer by adding a toolbar button (and keyboard shortcut) for this. Regardless of where you are on the page, regardless of website, you could always scroll to the top.
The second button might be a bit trickier to solve using contemporary standards and browser compliance. However almost every website has a main navigation of some sort. Most websites also has a sitemap. Both the sitemap and the typical navigation contains structured information that describes the structure of a website. Using this data it would be possible for the browser to present a standardized menu regardless of which page you are looking and no matter where on the page you are currently viewing. And if this is hard to achieve, the browser would at least be able to display the implemented html menu (by simply open it and scroll into focus). Either way on long pages and especially those websites with the mobile friendly “hamburger menu” would benefit of this button.