Those numbers are what I'd expect from a pool that is constantly being refreshed with ground water. Your spring has low saturation (low TA and CH) and so your pond will have the same. In an outdoor, pool stabilizer (cyanuric acid or CYA) is absolutely critical as it both buffers chlorine reducing its harshness on bather's skin, eyes, etc, and it also protects the chlorine from UV loss. With no CYA in the water, the chlorine has a half-life of about 30mins. So, if you add chlorine, it will more or less be gone in about 2-3 hours. On top of that, your spring water likely has some level of dissolved organic carbon in it and that will act as a source of chlorine demand. Top it all off with your persistent algae bloom (yes, your water has algae in it even if it looks clear) and there is no way to keep the FC up.
I'm not sure how much help we can be. Traditional pools are designed to be closed loop bodies of water that can retain chemical additives. Your pond is not that. The EPDM rubber liner is compromised and you're going to have to fix that or else anything you add will simply go to waste. In the short term you can keep adding chlorine and maybe even get a detectable level of CYA using liquid stabilizer as the source, but you're always going to be fighting a losing battle against the water loss. You have to get that liner fixed or else there's really no point in operating your pond as pool.
Also, as a chemistry aside, if you chlorinate water with a lot of organics in (carbon compounds from the input stream), the chlorine tends to react with those organics forming trihalomethane (THMs) compounds which are very irritating to be around (stuff like chloroform, etc). This is in addition to combined chlorine compounds from bather waste like monochloramine and chlorourea. So just dumping A LOT of chlorine in the water will not help and could very likely sicken people. This is why municipal water suppliers don't chlorinate raw water streams without doing significant filtration or else they'll create a larger problem.
As for pool putty, I have no idea if that will work on EPDM rubber. It's meant for cementitious pool surfaces.