"Is it problematic when a site has graphics for navigation?"

It depends. Most of the time it's still a link, so the browser has no problem identifying and highlighting it as such. If it's something fancy (image map? JS magic?)--it can be a problem. Fortunately, such sites are not common.

"Do you cycle through links and then choose the one you wanted, or is there a more direct way of accessing them?"

You press 'f' (for "follow") and a number appears next to each link. Then you enter a number to follow a link.

"Is it really faster than using a mouse?"

It depends. For example, there are whole WM environments which are designed to work without mouse (ratpoison, stumpwm, xmonad, etc.). Naturally, a keyboard-driven browser lends itself beautifully to such environments. Other than that, I find it annoying having to move my hand from the keyboard each time I need to look something up with a browser.

Of course, when I just surf the web, the mouse is usually more convenient.

"Do you need two hands to be efficient, and if so, wouldn't you rather be efficient with only one hand, for example using Opera's mouse gestures?"

Since conkeror is modeled after emacs, I'd say yes (unless you happen to be using a custom keyboard layout or something). As for the efficiency--again, it probably depends on the "mode" I am in (mouse is easier for plain surfing).

Besides plain, what other kind of surfing is there?

Or are you talking about the differences between using those keyboard-only WMs and normal ones?

As far as I know, using only the keyboard for some task is usually about efficiency gains, but in the case of surfing, I'm obviously not sure there's much to be gained, compared to mouse gestures.

On the other hand, if using only the keyboard is some kind of personal preference, that may leave something to be desired in other areas too.. Such as, a mouse :p

Working with online documentation while coding, for example, is much more efficient for me with conkeror. Or looking up some piece of information while I am typing a reply to a HN comment :)

On the other hand, it's an overkill for me to keep both my hands on the keyboard while I am reading a nytimes story or following links at leisure.

Fair enough :)

My wrists were sore for around 1,5 years because of bad ergonomy.

Opera has an excellent way to select links using spatial navigation (shift+down,+up,+left,+right). It's remarkably easy to navigate to any link quickly on the page.

Also http://www.opera.com/browser/tutorials/nomouse/ is a good place to start "keyboard-only" browsing.