8- Is the incident about 'Umar pushing a door on Fatimah (S) and killing her and her baby authentic?

There is no common consensus amongst the historian's concerning the way of martyrdom of Muhsin, the unborn son of Lady Fatimah al-Zahra (as). In Sunni sources the miscarriage of Muhsin has been mentioned, however nothing has been mentioned as to how it happened.

( however something was written by the great Historians Masoudy and Nizam narrating from Shahrestani). In the Shiite sources the more valid and stronger opinion has been that the martyrdom of Muhsin was the result of the lashes of the whip of Qunfudh (the slave of Omar).

For more information you may refer to book Bihar al-Anwar (vol.28).