What should a praying person who doubts having offered one, or two prostrations in the third Rakah (unit of prayer) do?
Whoever has doubts about their prayer should consider what is less i.e. the above person should offer another Sajda (prostration) and complete his/her prayer, then offer Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
A woman used contraceptive pills, and her menses exceeded (15) days, is it permissible for her to fast?
The maximum of menstrual blood is (15) days, but if it exceeded that due to a medication, or the like, then it is Istihadah (bleeding outside the monthly period), and in this case she should perform Ghusl (ritual bath), pray, and fast. Moreover, she is obliged to make up for the missed fasting days which exceeded her regular menses. And Allah Knows Best.
Talking to one's fiancée in Ramadan with romantic talk may lead to arousal, and if pre-ejaculate fluid (Madhy) is discharged as a result, it does not break the fast. However, it is advised to avoid actions that provoke desire and lead to this outcome. If semen (Mani) is discharged as a result, it does break the fast.
The discharge of Madhy doesn't invalidate one's fasting but it invalidates the ablution and his clothes must be washed because they are impure in this case. As for Mani, it breaks one's fast and making up invalidataed is obligatory, beside; a Muslim suitor should abstain from these matters during Ramadan and not to degrade the holy month to this extent. And Allah Knows Best.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.