Faraaidh of wudhu

Q: Could you explain to me how many faraa'idh are there in wudhu and what are they?

Q: After making wudhu in the morning and performing my Fajr salaah, I noticed that there was still some dirt around my eyes. Will this nullify my wudhu or salaah?

Q: During wudhu, whilst washing the arms, is it also fardh to include washing the hands too, or is washing the the arm from the wrist to the elbow sufficient as hands have already been washed previously at the beginning?

Q: After a persons has had a shower not faraz ghusal, does the person have wudhu even if he hasn't made the intention to make wudhu?

Q: Please advise me with regard to making wudhu with spray bottles, as I have been thought that the least requirement of wudhu is for water to drip off the limbs, when making wudhu.

Q: When making wudhu, how should the fingers be positioned during masah of the head? I have heard some ulama saying masah of head should be made with all 5 fingers with an open hand, or some say masah of head should be made with 3 fingers (middle ring and baby fingers). Please advise.

Q: I performed asr once, broke my wudoo, went downstairs and the banisters of the stairs have paint bits that come off onto your hands [not wet paint, its like white specks that come off] and then I made wudoo' and went back upstairs using banisters, prayed and when I finished after a short while of being in my room I looked in the mirror and noticed a small speck on my eyelid and this speck doesn't really take much to take off, even a rub does it and now what do I do? Do I assume my prayer's valid as it could have been either times, but most likely the speck would have come off in wudoo as you wash your face three times?

Q: Do males have to 'wash' their beard when performing wudhu or simply make khilaal of the beard?

Q: Is this true that Allah does not order us not to leave any dry place in wudu’ and ghusl. If one, though one has washed a limb, does not know that a
part on the limb has been left unwashed, that limb is assumed to have been washed completely?

Q: If one had applied oil to the beard or head, should one wash out the oil when performing wudhoo or ghusl? Or will the wudhoo/ghusl still be valid if there is oil remaining?