What really happened to Korra?

Honestly, I got the same doubts when I watched this season yesterday. However, I am going to try answering your questions. Please keep in mind that I didn't watch previous three seasons, so I might lack some knowledge about this bending world, so correct me if I am wrong somewhere.

Are all these events possible?

Apparently, they are.

Is it truly Amon's Blood-Bending that blocks the power or did Amon achieve what Tenzin thought impossible and learn Energy-Bending?

No. Amon used bloodbending to take away bending abilities. He was able to duplicate the Energy Bending which is possible to avatars only, using his bloodbending. My guess is that he does something to the blood flow (to the areas that correspond to bending) in brain, that probably disables those parts of brain which are used to control bending. He must have got this knowledge about parts of brain and the energy flow in brain etc. because of his additional knowledge about chi-blocking. We should keep in mind that he is the only person who knows both chi-blocking and bloodbending. Amon must have used these both successfully to duplicate Energy Bending in this aspect.

Amon also doesn't heal/restore his brother's bending abilities at the end. He could have let his brother have at least the water bending abilities so that he could help him in his next quest. However, he doesn't/couldn't do that. Energy Benders can restore these abilities. It seems Bloodbenders like Amon can't do this sort of thing (not yet). This proves that Amon didn't have real Energy Bending abilities.

And if so, how did bending Korra's energy take away all forms of bending except Air-Bending?

It seems that there are parts of brain corresponding to each bending ability. When Korra's abilities were removed, she didn't have the ability to air bend. Also, Amon knew what abilities she had/ didn't have. So, he must have probably removed the other three. Trying to unlock them might have led korra to unlock the one that hasn't been unlocked before, because she was in a situation where she needed to bend in order to save her love. So, she might have directed all her bending chi to the area which she never was able to direct to before. This could also hint that she was connecting to her spiritual self.

Now, if in case there was nothing like parts of brain for each bending ability - it could mean two things.

1. A person could do other form of bending that is different from what has been taken away. It means that a fire bender can learn water bending after their fire bending has been taken away.

   This is similar to alchemists learning Alkahestry in Full Metal Alchemist: Brotherhood no matter whether they still have Alchemy abilities or not.

2. Korra must have started connecting to her spiritual self even more strongly and learned the air bending ability from Aang. It was said in the series that Aang connected to his previous lives and had this immense experience behind him to ask from. Korra must have done that, and got the air bending abilities from Aang.

   This would mean that her spiritual quest must have started when she was in the metal container, and made her learn the air bending abilities in the process and finally led to her becoming a perfect avatar.

Regarding what Amon did under the assumption that parts of brain didn't exist, it would mean that Amon wasn't able to simulate the Energy Bending totally. We know that Energy benders have some special abilities among which removing/ restoring bending is a part. Amon should have been able to use his skill only in the removing aspect and not the restoring aspect. Even when he was a child, he says that removing is the best quality among all - this could mean that he must have concentrated on this single aspect and forgot/ disregarded the other ones.

It also means that Amon was never interested in learning Energy Bending, but only the removing part of it, the only thing he was able to do successfully. In any case, Amon didn't Energy Bend.