The answers are:
Q1. Phenotype of the offspring: mice with brown eyes. Genotype of the offspring: Bb.
Q2. Genotypes of the parents: male mouse - BB, female mouse - bb.
Since allele B is dominant over allele b, only one copy of B is needed for brown eyes, so we have following genotypes and phenotypes:
genotype       phenotype
BB Â Â Â Â Â Â Â Â Â Â Â Â a homozygote with brown eyes
Bb             a heterozygote with brown eyes
bb             a homozygote with blue eyes
A homozygous brown-eyed males  (BB) mates with a blue-eyed female mouse (bb). The offspring will get one allele from the father (allele B) and one allele from the mother (b):
Parents             BB    x    bb
Offspring         Bb   Bb   Bb   Bb
So, all of the offspring will be Bb - heterozygotes with brown eyes.