There are most likely several different things going on. Without good water test results it is difficult to figure what they all are. The best thing to do would be to buy a top quality test kit. I recommend a kit from TF Test Kits. The Taylor K-2006 is also good. Wile you are waiting for that to arrive, you can go to a pool store and get your water tested and report the numbers back to us.
I am fairly sure you have algae. Killing the algae is going to take a fair bit of chlorine. At this point I think that your simple test is reporting combined chlorine (CC) levels, which don't help keep the water sanitized. The FAS-DPD test, in the kits I suggested, can distinguish free chlorine (FC), which does keep the water sanitary, from CC. Chlorine normally needs to be added daily. Even in extreme cases, with very high FC levels, you can only go a couple of days without adding chlorine.
The Intex filters are not very good at all. Unless you get a better filter, it is going to take quite a while to clear up the water. Plus the real clearing of the water can't really start until the algae, if any, is dead. Many people have problems with their Intex filters. They are just barely usable. With persistence you can get the water clear, but it is going to take a while and lots of cleaning and replacing of the filter cartridge.
Feel free to ask more questions. In the meanwhile, do some reading at Pool School.