I personally test with salifert, but have used the Red Sea tests on a few occasions and they are equally suited for giving accurate results. If you by the alk, calc and mag kit you can also purchase refills for the reagents rather than buying the whole kit again which makes them cheaper long term than the salifert which is pretty cool.
Whatever you have been testing alk with up to this point appears to be highly inaccurate based on those numbers and what you did.If you like the Red Sea I would highly recommend grabbing their kits and you wont be disappointed. As far as their relationship to the nem it is mostly based on tank stability, and I would again recommend reading the link I posted above. It even has a great chart right at the top with a quick reference to recommended parameters levels, and the article goes on to explain in a basic way the overall role of each parameter in our tank and which ones are more important to test and dose for.
As for the chemicals to dose with, Red Sea is very high quality and would be a good place to start since your tank is relatively small the extra cost wont seem like too much burden in the short run. Once you get the hang of it there are cheaper versions which do the same thing.
Good luck, and keep asking questions as it is the best way to learn.
P.S. - The fact that one of the other nems died, his looks stressed, yours has been stressed and the other split (for a newly added nem this is also usually a sign of stress and is not a good thing) leads me to believe it was not the best batch of nems. However, like you said this has put you on the path to better water chemistry and that is a big positive.