Sunnah & Nafl Fasts

Fasting on a Friday

Q: A day before yesterday one of the elders in my family told me to fast after praying tahajjud on Thursday to make a specific dua to Allah Ta'ala. So I did, but today when searching through the net I found that it is forbidden to fast on a Friday? Is it permissible to fast on a Friday only?

Fasting only on the 10th of Muharram

Q: Some people say that it is not makrooh to fast only on Ashura, the tenth of Muharram, because it is no longer the practice of the jews in today's times. Rasulullah (Sallallahu Alayhi Wasallam) mentioned in the Hadith that we should not only fast on the tenth as we will be resembling the jews. Since the jews no longer fast on the tenth of Muharram, it will no longer be makrooh for Muslims to only fast on the tenth. Furthermore, they cite the following quotation of Badaai'-us-Sanaai' in support of this claim. Is this view correct? If not, then what is the correct explanation of the following quotation?

وكره بعضهم صوم يوم عاشوراء وحده لمكان التشبه باليهود، ولم يكرهه عامتهم