Conditions for the validity of Salaah

Q: I have prayed the Zuhr prayer today. But realised only after Esha prayer that my qiblah direction was incorrect. Do I repeat the salaah?

Q: I started praying Maghrib Fardh about 30-31 mins after Maghrib started (according to the calendar) and finished 41 mins or so after Maghrib started. I am not sure if I performed it on time as it was already dark outside. Do I make up the prayer or is it valid because my intention was to pray the fardh of maghrib? I also prayed 2 sunnah what about them?

Q: Is it ok to sleep before esha and then wake up and perform Isha before the morning? Is it right to perform Isha at 1 o'clock? 

Q: One has an atomic wrist-watch. That is a watch that runs exactly on the second with the atomic clock setting. If sunrise on the prayer calendar is at 7.00 and one finishes Fajr salaah at 6.59 and 58 seconds i.e. 2 seconds before 7.00 o'clock. Is the Fajr salaah valid? And what if it was finished 1 second before 7.00 o'clock?

Q: When does the time for zuhr end according to the Hanafi fiqh? Does it end when the Shaf'iee asr time starts or is it after?

Q: I have seen scores of pigeons roosting in many Masjids.  They keep flying around and a lot of their droppings are found on the prayer mat, some dry and some fresh.  I had the opportunity to witness so much droppings continuously being made by the pigeons roosting in Jama Masjid in Delhi during my visit once, when I had gone to offer my Dhuhr Salaah with the Jamaath.

I require the following clarification.

1. Is our Salaah valid if offered at such a place full of pigeons' droppings, dry or fresh?

2. Do we have to clean only the spot of the droppings if they fall on our clothes if we are in a state of Wudhu or do we have to do our Wudhu all over
again?

3. Similarly, I have witnessed the same scenes at many Eidgahs in different cities during my travel, during Eid Salaah, where sheep/goat droppings/cattle dung are found all around dry or fresh, which the people responsible for the maintenance of the Eidgahs neglect to clean. Is our Salaah valid in such places?  

4. What is the Shariah Ruling on these kind of najis?

Q: When praying at home where you are certain that there is no najaasat on the floor, will it be ok to pray directly on the floor? Or is it still better to use a prayer rug?

Q: About 2 months ago when I prayed Dhuhr in school, one girl changed the direction of the prayer and I prayed with her even though iI had severe doubts about if it was the right direction. I then found out that it wasn't the right direction but I didn't repeat the prayer. Should I redo the prayer? And is it as if I didn't pray? I had forgotten about this incident, it recently came to my mind, what should I do?

Q: I would like to know if the salaah of a female is accepted if her ankle becomes exposed (because of the knee bending) while in jalsa position although the pants or aabyah is long enough when standing?

Q: Please advice if a lady has a long dress or abaya on that is not see through must she still wear a pants underneath when praying namaaz?