There is no evidence to suggest that it is haram to eat duck or pigeons, so we go back to the original principle, which is that they are permissible.

If you fast the six days of Shawwal, you do not have to fast al-Ayyam al-Beed during that month too and hopefully you will be rewarded for that.

Scholars differed concerning the ruling on ‘Eid prayers: 1- it is a confirmed Sunnah; 2- it is a communal obligation; and 3- it is obligatory for men.

Shab e Barat is a bid`ah and there is no celebration in Sha’ban and there is no special act of worship to be performed in mid-Sha’ban or during the last days of the month. For more, please see the detailed answer.

Salat al-Raghaib is a bid`ah that has been introduced in Rajab. It is done on the night of the first Friday in Rajab, between Maghrib and `Isha, and is preceded by fasting on the first Thursday of Rajab.

There is no sound hadith to indicate that there is any special virtue in fasting in Rajab. But there is a report from the Prophet (peace and blessings be upon him) which indicates that it is recommended to fast during the sacred months. For more, please see the detailed answer.