Salaah

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: In some kitaabs like taalifat rashidiyyah it is written that it is mustahab to repeat the salaah prayed behind a faasiq (the one who trim or shave less than a fist lenght) and in ahsanul fatawa it is writen that if the salaah of a muqtadi become makrooh due to the salaah of imaam become makrooh. What is understood is that it is mustahab for the muqtadi to repeat the salaah prayed behind a faasiq. Please confirm?

Q: A person who is "saahibut tarteeb" was sitting in the jumuah bayaan when he realised that he hadn't performed fajr. He then planned that he will read his qada when everyone is reading their sunnats after the bayaan, before the khutba. However he had a dire need to go to the toilet and only returned when the Imaam was on the mimbar and azaan was called. So he sat for the khutba, read jumuah and performed his fajr qada after the jumuah salaah.

1. Is what he did correct?
2. If not, what must he do to rectify his actions?

Q: Please can you advise how many rakaats to be read for Tauhajud and can one recite any surahs and also how many rakaats to be performed together?

Q: When reading fardh salaah behind an Imam, does one have to read surah fatihah even if the Imam is reading surah fatihah?

Q: During tashahhud one says "..as salaamu alayka wa alaa ibaadillaah'is salihin.." instead of "..as salaamu alayna wa alaa ibaadillaah'is salihin..". Does this break salaah if left uncorrected?

Q: Is it permissible to correct the imaam during the qiraat in fardh salaah:

1. If the imaam makes a mistake which changes the meaning of Quraan?
2. Imaam jumps to another ayaat and realises this. So the Imaam starts at the beginning of the ayaat and still does not get it right?
3. Imaam gets stuck during recitation?

​Please explain also in respect to the 3 ayaats being read at this point and also if not?

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: Can a person pray salaah while wearing their glasses?

Q: Is qaza namaz acceptable if the prayer was skipped on purpose due to laziness?