Does microwaving eggs kill salmonella?

Microwaves do not kill bacteria, heat kills bacteria. The higher the temperature, the faster those bacteria will die off.

"Instant death" for most bacteria (including salmonella) is about 160° F (71° C). You only need a few seconds at this temperature. The notoriously strict USDA recommends 160° F for egg dishes but is considerably more lax about whole eggs and just says to cook until firm. Very few eggs are contaminated in the whites or yolks, so the risk is very low.

Pasteurization begins around 57° C (135° F), so many bacteria are killed before the egg coagulates (at 63° C / 145° F), which is why the USDA is not very strict about it; if an egg by itself is "firm" then it's generally already been hot enough for long enough to ensure safety.

Unfortunately, microwaves tend to heat (a) quickly and (b) unevenly, so if you are concerned about food safety and insist on making eggs in the microwave (not recommended), be sure to use short bursts and stir several times, otherwise you might end up with a combination of uncooked and overcooked parts, which is bad for food safety and for general taste and texture.

Note that there is not only a possibility but actually a certainty that some salmonella is still there, assuming that there was any to begin with. Cooking is equivalent to pasteurization and that does not kill every single bacterium, nor is it meant to; it just kills about 99.9999% of them which makes the cooked item safe enough to consume.

Not necessarily: http://www.nytimes.com/2007/05/22/health/22real.html?_r=1

However my guess is that the heat generated by a microwave would be hot enough to kill most of the bacteria (backed up by some of the research in this article: http://www.straightdope.com/columns/read/2947/do-microwave-ovens-kill-bacteria), so as long as it's a fresh egg the risk of salmonella poisoning is low.

If you're using pasteurised eggs, you should be fine.