No problem
I am glad you have chosen to ask a shia muslim about shia islam, because you can often get biased and particularly veiled responses from a non-shia who disagree's with shia islam.
Now, the question of 'hitting' oneself is often asked and i have addressed this in the first page. Today you'll find a minority of shia's as you have probably seen in the news, taking blades, or whips with little blades, and cutting and hurting themselves. This practise has absolutely no religious nor rational basis, and many of our ulema, from Ayatullah Khomeini [rh], to Ayatullah Khamanei, to Ayatullah Fadllulah [rh] have forbidden this practise. Unfortunately, culture and tradition have infiltrated many madhabs and many religions, but inshAllah, due to the many movements being made to help eradicate this rather recent innovation practised among a minority, we may see it continue to decrease in popularity.
Now, you also have shia muslims who use their hands and hit their chests. If this is done in a way that is civil, it does not constitute self harm and is more of a symbolic sign and show of sadness. It is also important here to note that this is not the 'prescribed' way of commemorating, but it is cultural, and culture can have a place in islam so long as it does not violate the tenants of the religion. I study medicine and i've personally dissected the chest area, the ribs, the sternum, seen the arrangement of the organs and have had to study many potential cases of trauma that can be a cause of harm. Hitting your chest, if done in a civil way, will not cause any harm at all. You see, it alludes to symbolism which you want to emanate and be reflected to everyone in the outside world. It is essential here to note, if someone takes their top off and starts to really hit themselves hard with both hands, such a practise should be discouraged and i personally am against that particular way.
Now, shia's essentially remember the Grandson of Muhammed [saw], Hussain ibn Ali [as] who is regarded by all sunni's and shia's as the leader of the youths of paradise [we will all enter heaven as youths, no-one there will be 'old' or an 'elder'].We also remember the family and close companions of the Prophet[saw] who, in Kerbala were slaughtered, mutilated, beheaded, and the women and captives taken in chains. The caliph of the time was the evil and despotic man , Yazid ibn Muawiyah ibn Abi Sufiyan.
We don't necessarily mourn for the particular 'deaths' as we do collectively for the absolute way the ummah deviated, and how rife injustice was, and what calamity befell the Ummah, that only 50 years after the death of the Ummah, such an evil and despotic man essentially occupied the very same seat of power as the Prophet[saw].
Furthermore, according to traditions accepted by both shia and sunni muslims, the angel Jibrael forewarned the death of Hussain ibn Ali a.s, which caused tears to swell in the eyes of the Prophet [saw].
Narrated Muhammad bin Udaid, narrated Shurahbil bin Mudrik, from Abdullah bin Nujayy, from his father, that he traveled with Ali , and he used to carry his purifying water. When they were next to Nainawa on his way to Siffin, Ali called, “Be patient Oh Abu Abdillah (the kunya of his son al-Hussain), be patient Oh Abu Abdillah by the banks of the Euphrates. I [Nujayy] said, “what is this?”. He [Ali] said, “I entered upon the Prophet one day while his eyes were shedding tears. I said, 'what is it with yours eyes shedding tears?'. He said, 'Rather, Jibreel was here earlier and he told me that al-Hussain will be killed by the bank of the Euphrates and he [Jibreel] said 'do you want me to provide you a sample from his soil [where he will be killed] so you can smell it?' and I said 'yes'. So he extended his hand and he took a grip from the soil and gave it to me so I couldn't help my eyes to fill with tears'”. [Recorded by Ahmad, vol. 1, p. 85.]If you have time, check out this video
[video="youtube;RnRtt83RY0w"]https://www.youtube.com/watch?v=RnRtt83RY0w[/video]