Yes getting a test kit for alkalinity would be a good idea, testing alkalinity is one of the more important tests for corals.Yes but I don't have a test kit for it yet. Should I get one and test for alkalinity?
Nothing on your parameters stand out to me as being horrible. The only thing I will say is that when I first got corals and my nitrate was 0 I was never able to keep corals happy. So I'd try to get your nitrate up some. I try to keep nitrates somewhere around 5 personally. I would also raise your salinity a little, most tanks with coral are kept around 1.025-1.026.
I would think any water parameters that would make the duncan unhappy would effect the hammer coral as well. Duncan's are one of the hardier lps corals.