Does one need to perform two Chi-square tests?
You should just have 1 chi-square test to test the hypothesis.

Note that the problem is asking about F2 generation, not F1.

H0 in a chi-square test is your prediction based on a model; H1 is that the real outcome differs from what is expected, so you have that a little backwards. H0 should be the expected counts knowing the initial proportions and expecting autosomal dominant inheritance.

Start with your prediction:

F1 generation will be half heterozygous males/females, half WT males/females, so F2 generation has 3 types of mating events:

Cc x Cc occurs 25% of the time, and 75% of offspring are affected

Cc x cc occurs 50% of the time, and 50% of offspring are affected

cc x cc occurs 25% of the time, and 0% of offspring are affected

Multiply these probabilities and you should have 43.75% expressing the phenotype; your prediction for the chi-square test is that you will see this same percentage regardless of sex.

From there, doing a chi-square test is simple and there are many many resources online for this (here is just one).