Who is Ginjin Kuugo?
What do he and his companions "know" about Urahara and Ichigo's Family?

erm, if im not wrong, hell arc is for the movie, this current arc in the manga is the "lost shinigami power arc" or wadever thing they call.

It's just me or it seems like this Kuugo guy really want Ichigo to join him??...

I think that they want Ichigo in their group because he is the only person born to all three races, human, shinigami and hollow. (his dad was a shinigami who became a human and his mom was theorized to be a hollow)

Time reversal? Using healing kiddo to restore his spiritual integrity via pouring in riatsu? Shinigami Power Transfer? The Hogyoku? Kubo Reality Manipulating? Take your pick.

I have a basic idea of how Ichigo could get his powers back

Basically, it is using simple physics (i know that's an oxymoron) as a basis, speicifcally the Laws of Thermodynamics.

Since energy cannot be created or destoyed, only be changed in form, Ichigo's powers must still exist, to some extent, in his soul. Given that the "fullbringers" can use  a soul to release it's full potential, they can pull that ability out of him and he will get some limited powers which will regenerate if put in a spiritron-high location like, oh, say, Soul Society(let's face it, after taking out Aizen, Ichigo can call in a few favours with the higher-ups)