What matches are taken into account to compute those stats ?

All normal and ranked 5v5 games, from the last 30 days, are taken into account to compute the stats.

How do you determine what role a player is currently playing ?

Using the data I have (global champion usage + each player history), I try to find what is the most probable role distribution. This may be sometimes wrong, but well, who would have guessed that Smite Janna Top is a thing ?

Where do you grab your data ?

Riot APIs !

What is this rank displayed alongside my current ranking (gold in soloqueue for instance) ?

This rankings aggregates Riot ranking in all regions to get your rank. (If you are Gold IV, you'll have a better rank than a Gold V player for instance). This rank is updated almost in real time.

What is this rank displayed alongside my champion ?

This rank uses the leagueofgraphs.com ranking mechanism, which is based on global rank (silver, gold...), kda, winrate... Have a look at leagueofgraphs.com website for more information.

What kind of partnership do you have with leagueofgraphs.com ?

I'm the creator of League of Graphs :)

I have a question, how can I contact you ?

Have a look at the contact page !