Firstly: this question is addressed to SHIA muslims...right??? then why on earth others are replying on our behalf... that is your never-ending dictatorship, you have to control our thoughts and opinions and answer for us.
dear asker: in regards to your questions I shall answer them to MY knowledge as a SHIA muslim:
1-only few bleed their heads on the day of ashura to show sympathy for the tragic events of karbala caused by Allah's enemy Yazid the son of Mu'awya...he seiged the camp of imam Hussien(as) killed all his sons, his relatives sons, his friends...etc
the women were tied to ropes and were taken to different cities of Iraq, Syria, Lebanon..etc (remind you these women are the granddaughters of who???? the prophet(pbuh&hh))) ...up to this point if you think islam was still the same, then you are definately misguided..
2-we pray on stone because it is a different translation of the hadith we muslims share..(God made earth for me a place of sujud)... we translated earth as basically earth (sand, mud, stones, or what grows from it i.e plants leaves....etc) we do not pray on mats made by man in unnatural ways... we use any sand to make disk like shapes to pray on coz that way they are easy to take with you whenever, and you dont have to fill your room with sand...
we use though, the sands of karbala, because we think that site is holy(site of the great massacre), but we dont worship it...etc like some people would say..
3- we don't curse in the way you imagine but we condemn Aisha, Omar, and Abu Bakr
Aisha: for waging war against imam Ali leading to the deaths of 10,000s of muslims when she is supposed to be the mother of believers...(a mum that kills her children is not a great of a mother right??) she also declared hatered towards imam Ali(as) read her response when she heard he will be assigned a khalifa.....pretty weird huh??
HOWEVER WE DON'T CLAIM SHE CHEATED ON THE PROPHET AND MA GOD KILL THE ONES WHO SAYS THAT, im not saying that because I like aisha (in fact I dont) but i say it to defend the prophets reputaion as we know that the honor of prophets is protected by Allah(sw)...
the hadiths you will find in our books about how she cheated are taken from your books only to illustrate how you are stabbing the prophet's honor... i.e we condemn those hadiths in your books not support it.. (by the way the people who claimed she cheated were SAHABA, which obviously means not all sahaba were good...agree??)
as for the other 2 people Abu bakr and omar respectively:
we believe they conspired to steal khilafa from Ali(as), thus they purposely missed the prophet's funeral to go to the meeting..etc
as a proof notice when imam Ali(as) made alligance and how?? about 6 months later....why that long?? and WHAT HAPPENED ON THAT DAY???
plus,
wonder why the prophets daughter Fatima(as) the wife of Ali(as) dies in less than a couple of months after her father??? why happened and why she died?? why is omar connected to this??? coz we have evidence which u may never approve of that he was the reason for her death....
finally, read the speech of Fatima(as) which she made to the people, and you will find out why she died, and why shi'as are opressed and the real story about the sects...
wa ssalam