Alexa can be very hard to understand, only because of the way it records rankings. For example, the site in my sig, has a low alexa ranking because of a short period of low traffic (due to writers taking vacation). Shortly after, some new sites linked to it, and the traffic rose exponentially, and so did Alexa's line-graph chart. However, it's still 300,000 ranking but this is misleading, because it's 3-month ranking. If you look at the one-month, the ranking would be 100,000. In fact, if you look at like "2-week" ranking (too bad it doesn't exist), I bet it would be 50,000 ranking. Watch in about 1 month, the ranking will rise exponentially, because Alexa is playing catch up. So don't put your hopes down. You'll see your site grow quickly if you keep working on it. You shouldn't have to worry about your Alexa ranking, because if you're doing a good job, the Alexa ranking will follow (a bit slow tho).
Alexa raning is world wide. There is no surprise if your traffic is keep on increase but your alexa ranking maintain the same because the website list better then you are getting more increase in traffic
Nobody should consider Alexa an authority on anything. Their stats are completely inaccurate and useless.