Alexa is completely inaccurate and easy to fake, it basically means nothing. If you're considering buying a website, DON'T even look at Alexa, ask for stats from Google Analytics or something from the server like AWStats.
There is much doubt in alexa ranking. So count hundred percent accurate traffic for a month is not easy task. Even tough you can count traffic with many other online tools.
You're right that Analytics is the best stats to look at when considering purchasing a site but Alexa isn't totally useless. It's good in a general info way. Sites ranked 100,000 and above have enough people visiting them that have the Alexa bar installed for it to be considered a reliable indicator of traffic levels.
Yes you are probably correct. I noticed someone selling a site (in the websites section) claiming to be getting 100UV a day then when I checked alexa stats around 40% of the stats came from India! so it probably had something to do with the alexa toolbar.
alexa is just telling you to use more alexa tool bar to get better rank, in simple don't rely on alexa for traffic its a mumbo-jumbo, just a fun tool for me for smaller sites (at least)
I can get a site with 0 legitimate traffic into the top 100,000 in a few weeks...so no, that isn't a "reliable indicator of traffic levels" either.