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.
What should one who forgot to offer the second Sajda during congregational prayer, and remembered it before the end of the prayer do?
All perfect praise be to Allah, The Lord of The Worlds. Whoever forgets a pillar of prayer while in congregation must follow the lead of the Imam, and after the latter offers Tasleem, he should offer one Rakah, then perform Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
Is there zakat on social security savings (retirement benefits)?
If the retirement benefits are received, zakat is due on them for one year. Before receiving them, they are not in the person’s possession to be liable for zakat. And Allah Knows Best.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.