Can one perform the Salatul Hajah (Prayer of Need) to seek marriage, and will the wish be fulfilled within a week, and is its non-fulfillment evidence of a weak connection with Allah, and what is the number of its rak'ahs and how is it performed?

It is prescribed for Muslim men and women to pray two rak'ahs known as Salatul Hajah (definition) (the Prayer of Need) when they have a need. It is permissible to perform it for any need, and there is no harm in repeating it. A Muslim should not rush the answer or consider it slow in coming, for Allah may delay the answer due to a wisdom He knows. The delay in an answer does not indicate a weak connection with Allah. Indeed, supplication (du'a') is an act of worship, and it is mentioned in the Hadith (definition) that Allah grants the supplicant one of three things: hastening the supplication, storing it for him in the Hereafter, or averting evil from him. One must be wary of rushing in supplication and of abandoning supplication.