It's been a while and I was always a bit shaky on the actual genetics, so hopefully an actual expert can weigh in here, but as far as I remember -
For 1 it depends on the penetrance model (a score on whether all individuals with the disease allele(s) express the disease phenotype: 1=all, 0.5=some, etc.) along with whether the allele's mode of inheritance is recessive/dominant, X-linked or not, and how consanguineous/inbred the pedigree is.
If I remember it right, if a father/son combo always express the disease allele, then the pedigree is x-linked recessive. If you see an uncle/son combo, and test for it, and the linkage score for the region of interest (the likelihood that the disease travels with the ROI computed over all individuals) goes up, then it's pretty suspect.
For 2, you could see the distribution of alleles without much computation. Siblings are expected to share X%, relatives Y%, unrelated Z%. By fitting to these bands, you could already see if the distribution of alleles was suspect. We never tested for mtDNA though, I don't think there were many chipsets for it back then.