The mannat of Bibi Fatima is that once your mannat has been fulfilled, you read the story of Bibi Fatima and then distribute sweets amongst women and children only. Isn't this the sort of a thing that people do when they go to Data Darbar? Isn't this a form of 'shirk'?

I think there is no need to comment on such a senseless practice. The thing, however, which needs to be kept in mind is that making religious vows (nazar/mannat) in itself is something which is discouraged by Islam. It is not a very sound approach to make good deeds conditional to certain results of the future if they come out be as a person desires. The Prophet (sws), it is known, never made a vow.

Of course! making vows is not forbidden. In fact, if a person happens to make one he should go on to fulfil it. The Prophet (sws) has said that all vows which result in the disobedience of Allah or are against Islam as well as sense and reason must be broken and must also be atoned for. This atonement (kaffarah) is a punishment for being irresponsible and is the same as that of breaking oaths mentioned by the Qur’ān (See 5:89).