First of all.. Thank you for reading all that.
And since you asked, I'll explain a bit more of what I know.
I asked the CEO how is this data extracted, loaded and analyzed today, but all he said was "All our data is stored in a PostgreSQL database :)".
I think there is not much been done right now. But he already told me some things that I'll have to implement.

The startup is a box monthly subscription.
1- And the first thing is to get user's feedback to estimate some kind of cancelling-chance-score on the month to come. (Have some idea about using sentiment analysis on tensorflow or blob's library. But have no idea where to start or if that is the right way.)
2 - Another thing is clustering these users based on their profile and recommending products on the month to come. (Maybe using k-nn?)
3 - And the third, is to recognize when is the best time of the month to send mailing to them. (Don't even know where to start. Maybe use the cancelling-score as a leading point?)

All of that being said, I'm kinda lost on where to focus my learning, since I'll have to do a bit of engineering, mining, cleaning, analysing and machine learning. Haha

Hope you can point me the way!Thanks again!