After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.
What is the ruling when the monthly period when exceeding (15) days?
The maximum duration of menstruation is 15 days. If it exceeds this, it is considered irregular bleeding (Istihada). In this case, one must perform ghusl (Ritual bath) after menstruation, pray, and make wudu for each prayer after its time begins. She should return to her previous menstrual habit regarding duration and timing. For example, if her period used to be from the 20th to the 27th of each month, this is considered her menstruation period. Anything before or after this is Istihada, during which she only leaves prayer and fasting for the habitual menstrual days, then performs ghusl and resumes praying.
A woman didn't fufill fasting of the month of Ramadan two years ago, due to pregnancy and breastfeeding, at the time being she is making up the missed Ramadan. What is the ruling of Sharia? And what is due on her?
Whosoever break the fast during Ramadan or didn't fast at all due to health concerns, is obliged to make up the missed fasts whenever she could so long as making up missed Ramadan didn't extend to the coming one, and if next one arrived without fulling fasting the missed one, the ransom is 60 grams for each missed day (Equals 60 piasters to one Dinar for each day). And Allah The Almighty Knows Best.
Should one who doesn`t perform prayer out of laziness make it up later, and how should he/she do so?
All perfect praise be to Allah,The Lord of The Worlds He/she is obliged to make up missed prayers by offering with each obligatory prayer another one, and if he/she offers two, then it is better. And Allah Knows Best.