Is it alright not to indicate the name of the father on the baptismal request due to some personal reasons?

As they say, it takes two to tango. It takes a man and a woman to conceive a child, thus a child will always have biological parents. If for some personal reason the mother does not want to include the name of the father on the baptismal record, refer this case to your parish priest for further verification.

Where can we get the baptismal certificate of children who were baptized through emergency baptism? Can they be baptized again?

There are provisions in the Canon Law related to emergency or conditional baptisms. A baptismal certificate may be issued also for conditional baptisms to include a remark that the baptism is conditional.