Do you know your CYA level? That is something important that we will need to know. It could be that it is really low and that would explain why you have a hard time keeping chlorine in the pool. For now, you should add some bleach to get some chlorine in there. In this size pool, each gallon (4 quarts) of plain 6% bleach will add about 2.3ppm of chlorine. Until we know your CYA level, we won't really know how high to tell you to take the chlorine, but for now, I'm going to suggest taking it up to about 6. You many need to add bleach a couple of times per day to keep some cl in there.

Your pH is good, your alk is low. Bump it up a bit with some baking soda. Add a couple of pounds at a time slowly through your skimmer. Test it again a few hours later and continue small additions until your alk is between 80-120. This is not critical. You can do this gradually over several days.

Do get that good kit. That will help you a lot. Post your CYA reading. (If your kit can't measure it and most likely it can't, go to a reputable pool store and ask them to test it for you. Just don't buy all the stuff they are going to try and encourage you to get.)

I am also going to move this post into the Saltwater section of the forum. There you are more likely to get good advice since you have a SWC. Hope this helps some.

EDIT -- Looks like Janet was posting as I was typing.