As I saw that Latestweets is Joomla 1.6 native, I decided to pay 10$ for it.
And I don't regret it.
As I do had some problems with the module (I had to set "No caching" for the module in it's parameters), the support was so prompt, I never experienced before.
I had a life chat through Skype with onscreen demonstration, and everything went smoothly.
Great job, Vipin!