Your equity would be ~12/46, so slightly more than 24%, but yes that is correct. Ideally you would input the range of the villain into an equity calculator like Equilab to get it more precise and also remember to take into account rake if the rake is non-negligible.
For your second question you are also correct under the assumption you have to hit the 6/A/diamond. I've put an example of Equilab below.