Sujud Ash-Shukr is done in response to a calamity that is averted or a blessing which comes to a person. There is no specific du`a narrated in the hadiths for Sujud Ash-Shukr.

In the cases where a menstruating woman is permitted to recite the Quran, she is also permitted to do Sujud At-Tilawah, if she happens to recite or hear a verse where the Sajdah is prescribed.

There are fifteen places in the Quran where we should perform sujud al-tilawah (prostration of recitation) when reciting them. For more, please see the detailed answer.