Summarized Fatawaa
• Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it ?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
• Does Istigfar(saying astagfiru Allah) between the first and the second part of Friday prayer`s sermon render the prayer invalid?
Talking during Friday prayer`s sermon is disliked, but there is no harm in offering Istigfar between the two parts of the sermon, and it doesn`t invalidate the prayer as it is actually from Sunnah.
• Is a woman`s nephew by suckling considered a Mahram( i.e. unmarriageable)who is permitted to accompany her to Hajj?
All that is prohibited by lineage is prohibited by suckling, and a nephew by suckling is a Mahram like a nephew by lineage ;therefore, it is permissible for him to be a Mahram for his aunt in Hajj and Umrah.
• Is Zakah(obligatory charity) due on the equipments used in the trading process such as: cars , shops etc..?
No Zakah is due on equipments used in the trading process such as cars and the like.