If an individual is homozygous for a trait, what percentage of his/her gametes will carry that allele?

100% will have that allele. Homozygous means the alleles are the same for every gamete, for example looking at Mendel's pea plants, if the allele for the trait of growing tall is T and the allele for growing short is t, a homozygous tall pea plant would have the genotype TT, meaning all of its alleles are tall