How does a Shakespeare play like Othello present the main characteristics of Tragedy? Does it bear any resemblance to Seneca and Aristotle?
The simplest answer to your question is yes, Othello does show connection to the classical definition of Tragedy. Aristotle, in his Poetics, laid the criteria out first. The main requirement that a Tragedy must fulfill was that something must happen so that, by the play's end, the audience is filled with pity and fear for the tragic hero. This, Aristotle says, will lead to an emotional catharsis for the audience, which should be the aim of the performance.
Othello is a tragic hero who undergoes a magnificent downfall due to succumbing to his tragic flaw -- extreme jealousy. He might be different a bit than the more tradtionally Greek tragic hero like Oedipus who is sole master of his demise, however. In Othello, Iago plays a very large part in instigating and fanning the flames of Othello's jealousy.
Yet, Shakespeare manages, even today, to fill audiences who witness Othello strangling his own dear love Desdemona in their bed with pity and fear. Even as he learns the truth and takes his own life, we feel pity for Othello who's been led astray by his weakness, and fear that we ourselves could, under certain circumstances, be carried away as well.
So, Othello can definitely be considered the hero of a classic Tragedy, one that adheres to Aristotle's demands for the downfall of the hero inspiring fear, pity and catharsis in the audience.