Does Istigfar (Asking Allah for forgiveness) 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. And Allah Knows Best.

What should a person, who doubts the validity of his Wudu, or over performs it, do?

One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.

Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?

It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.

A man has married a second wife and deprived the first from provision and overnight stay. He spent most of his time and wealth on his second wife. After sometime, the latter got sick and was diagnosed with breast cancer, which made him forsake her in bed and return to his first wife. What is the position of Sharia on this?