Keyword research tool?
 

Such keyword tools as wordtracker, wordstream has are now payable and quite expensive. Do you know any good free or at least cheap keyword research tools of similar quality as wordtracker?

Google adwords keyword tool.
Google Trends
Seomoz

Market Samurai is what you need.

See about keyword research here Keyword Research Video

We also have a heap of Keyword research videos and tutorials at Fast Web Insiders

Based on your experience, do you think global monthly searches on google adwords is a real number?

It's about as accurate as it gets. The key here is to focus on relativity not the individual numbers, for example if rude girls got 5000 top rank traffic per day and nasty girls got 7500 then the best you could deduce is that nasty girls was a slightly better keyword.

When it comes to the individual numbers, they are highly variable. If you rank number one for a keyword getting 50 SEOT per day as reported by Google it's unlikely you would actually get that number in practice.