Thank you for your kind words, pchela! I am very excited! He is such a sweet bird!
So, I let him out of his cage for about an hour. At first he was a bit hesitant and he flew a couple of times away. Both of the times he landed on top of the dome which made things a bit more complicated. The cage is huge and I wasn't able to make him step up because I could hardly reach him so I took a perch and he stepped up without a problem. I let him stay for some minutes on the playtop (he wasn't interested in any of the toys I had there) to calm down and then I tried again and he didn't have any problem stepping up. I let him sit on my hand for a while and then we did a bit of training (if you can call it training). I tried to teach him to step up on command. I did this for a couple of minutes and then I just let him sitting on my hand or my shoulder. The strange thing is that he didn't bite me not even once and he didn't have any problem with me petting him. I also talked to him the whole time and after a while he started replying to my voice. I also played some tunes at the piano while he was sitting on my shoulder. It was fun! I think we both did great for our first time!
I took some photos of him and the cage, but none of them were good (both because of the lighting and my ugly skills in photography). These two are the best, but still not satisfying. I will take more photos of him tomorrow morning.
Fortunately, I am sort of a cleaning freak so I think I won't have too much of a problem disciplining myself... 
