I haven't had a chance to try this out myself.

For menus and toolbars, do any of the usual "drag in from the edge" actions work? Or the equivalent "mouse pointer in the corner" method?

Which home page links aren't working -- the built-in Firefox home page?

You can to some settings from the charms bar right side, privacy and crash reports. In the app itself there is no menu. When it opens form the Metro side of windows it show a start page with tiles/links for bookmarks recent history top sites but the links don't open and there is no menu bar. Not sure if it a Surface issue or the beta.

the tabbar and the address bar with a menu should show up when you swipe in from the top or bottom like on other windows 8 metro apps...
http://windows.microsoft.com/en-us/windows-8/getting-around-tutorial

as for the links not working, this certainly doesn't sound right - do you get any sort of error message or does the app just not react at all once you tap on a tile?

Swiping down shows a window displaying the open tab and + sign which when touched will open a new tab same as the existing one. No address bar or anything else. The tiles in the start page depress/move when touch but nothing happens. No error messages or crash. Desktop version works as usual.

DaDD58, I talked to a developer in the #windev channel, and this is not something that they have seen before. Please try to start it in safe mode or disable all of the add ons to see if this is interfering with it. If it is, this is also useful to add to the bug I filed. Bug 976849 - Touch not working on Surface[user storyNo address bar The tiles in the start page depress/move]

It could probably use a better title too. Please add a screenshot to what you are describing if you can to that bug.

I assuming you mean start in Firefox safemode, not Win8 safe mode?