Impurity on body, clothes or place of Salaah

Bleeding piles

Q: What is the ruling regarding bleeding piles and salaat. Recently I was on a trip to Cape Town. Before returning, I performed salaat at the musallah at the airport where I was the imam. When I returned home I noticed that there was some blood on my underwear, which was from piles. I am not sure at what point the piles were bleeding. Please advise what action/s need to be taken, if any, regarding my salaat and that of the jamaat.

Pigeon droppings in the Musjid

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?