Since we have two genes for each trait, a person who is type B can have either two genes for B and is considered homozygous, or, they can have one B gene and one O gene. This will still produce a person with type B since the allele for B is dominant to the allele for O. They are considered heterozygous for type B blood. The other person is type O which is a recessive trait. That person's alleles for blood type are two O alleles and they are homozygous for type O blood. Therefore, if you cross a person who is BO, with a person who is OO, 50% of the offspring will have type B and 50% will have type O. It is possible then, to produce type O offspring from this mating. The other part of this question is regarding the Rh factor, another blood antigen. People with the antigen are said to be Rh+ and people who do not have it are Rh-. Rh+ is dominant to Rh-. Therefore, if a person is Rh+, they can have two alleles for the Rh factor and be homozygous, or, they may have one Rh + and one Rh- allele and be heterozygous, but their blood would still be Rh positive. Therefore, the parents in this problem must have been heterozygous for both type B blood and Rh factor, and the other parent was homozygous type O but heterozygous for the Rh factor. Since each parent had a recessive Rh- gene, these were passed to the offspring making it Rh-.
Yes they can if the genotype is BO+- and OO+-, you only report phenotype here - what we see, and genotype can hide the recessive Rh type.
So possible blood types from that combo, B-, B+, O+ and O- as the parents could be BB++, BB+-, BO++ or BO+- and OO++ or OO+-.