Hi Valeria
Welcome to the forum. Lovely to have someone from Romania here!
I don't know / have opinions on all of the questions you've asked, so I'll just answer those that I have some idea about.
Valeria wrote:Should I worry about the nail absence ?
Generally, the bird will function just fine without one toe nail. It's unfortunate but sometimes a bird will have one of their toes ripped off - usually be another aggressive bird. Have you ever noticed that he has any troubles gripping perches or branches? I think that could possibly be the main problem that could be associated with a missing toe nail.
Valeria wrote:From last year to now, Paco (this is his/her? name) learned to say "mama"(mother), "pacopa", "ai papat"(you ate?) ..
That's lovely.
Valeria wrote:But I can't touch him .. is very scared. How can I make him to like me?
When I'm cleaning the cage he is not aggressive with me, but when someone else try to put the hand inside he becomes nervous and start to struggle.
It sounds like you have made some progress with him yourself, which is very good. So keep doing what you are doing and just try to gradually make him a little more tame than he is already. Talk to him, let him observe you doing things in your normal day (without him being the centre of your attention), share your food with him, offer him treats through the cage bars. Find out what his fav foods are and withdraw them from his normal diet and use them as treats. If you want to, you can also try trick training. Once you have him accepting food from you from between the bars of the cage. Next you get him accepting food from you when your hand is inside the cage - then you're probably ready to try to teach him to perch on your hand. Not all birds will like petting, so you may never be able to pet your bird, however you can definitely get him a lot more tame than he is now.
Valeria wrote:Also, when I put seeds in his bowl, he throw it down. He may not like them?
I'm afraid that's just a natural birdy behaviour. It seems very wasteful to us... but in nature, that's one of the ways seeds get spread.
Valeria wrote:This morning I inspected his neck and I saw that begin to appear a small black spot under his beak. This means the ring should appear?
It could be - only the boys get a black ring. A photo would tell for sure. However, I'm sure if you're just starting to see it come through, there will be more black feathers joining it soon.
Valeria wrote:Beside the IRN, I aso have 3 budgies and when I leave Paco free, he goes straight to attack them. why is it so wild?
Unfortunately this may never improve, although it may once he is more comfortable with you. I wouldn't keep your budgies in the same room with Paco when he is out of the cage.
Best wishes Valeria!
Ellie.