I've tried to install Adobe Air 2.6 and then the old version of TweetDeck (0.38.2) but it's not working to me. Can anybody help me please?
You can get it working not too hard: make sure to read through all the steps first
Adobe Air for Linux is no longer supported by Adobe. Their 64 bit support was pretty bad to begin with. The chances of you getting this to work well are pretty slim. I would recommend just using wine.
You can use the older version of tweetdeck by installing air in wine then installing tweetdeck. This should work quite well (though it's obviously not ideal).
You also install the newer version of tweetdeck via wine.
Here are some links to get you started.