I am generating a new mouse model and want to determine which of my animals are homozygous by testcross with wild-type animals. How many offsprings do I need to be certain that the parent is homozygous?

Usually test crosses are done with a homozygous recessive. That way you know in the F1 if the parents are homozygous. Do that with WT and you mutated strain. Then you can just cross those same parents with each other.

Yes. I agree with Ringer. A test cross is between an unknown dominant genotype and a homozygous recessive in order to determine if the subject is heterozygous or homozygous dominant.

 

I have never worked with mice, so if I were you, I would look at the literature. See if, in the methods section of a paper, they mention "out of ___ number of progeny, _____ number were this phenotype and blank number were this phenotype, so the individual was deemed ___ genotype." You may have to dig deep into older literature, because I don't think this is very common anymore to include in papers.