Hardy Weinberg Equilibrium after 5 Generations
You are almost correct, but with a few modifications/comments.


The calculations in Q1 are independent of HWE, and are just calculating the current allele frequencies in the population based on genotype frequencies (i.e. would be the same irrespectively of if the population is in HWE or not).
In Q2 it is unclear if the questions is asking for genotype frequencies or allele frequencies. Your answer of genotype frequencies of $p^2=0.42$ ($a^+a^+$), $q^2 =0.12$ ($a^-a^-$) and $2pq =0.46$ ($a^+a^-$) is correct if you assume the allele frequencies from Q1 and HWE. However, your allele frequencies are incorrect and should be $p = 0.42 + 0.46/2 = 0.65$ and $q = 0.12 + 0.46/2 = 0.35$, i.e. the same as in Q1. Remember that the allele frequencies shouldn't change under HWE.
Yes frequencies should not change in Q3. This is the textbook definition of HWE, i.e. that allele and genotype frequencies remain constant between generations in the absence of evolutionary forces (i.e. under the HWE).