Is it permissible to marry a girl who was suckled by the suitor's mother, but the number of times she was suckled is not known, given that the girl's father used to keep her away from being suckled by the suitor's mother?

The mere fact that this woman's mother is your paternal cousin does not legally prevent you from marrying her. The preponderant opinion is that prohibition by suckling is not established except with five full sucklings. If there is doubt about the existence of suckling or its number, the prohibition is not established because the original state is its absence. Nevertheless, it is more cautious and absolves one's responsibility to avoid marrying someone for whom the conditions of suckling are not fully met.