Hi, and welcome to our forum, BRI! Unfortunately, in most of the country pools are closing or closed so our "throughput" lately has been a little slow.

Let's look at your numbers:
FC = .5 or 0 It's .5, which is not going to fight off algae given your CYA level (which I must question--more below). If it was .5 and TC was .5 it'd be better.
TC = 1 TC = FC + CC so, if we have FC and CC, we know TC. If we have FC and TC, we know CC. So let's cover it in CC.
CC = .5 The ideal CC is 0. However, when FC is positive, we frequently have CC indicated of .5 or less. If you re-run the test using 25mg of water rather than 10, each drop equals .2, not .5. Sometimes then, the .5 or less now looks like .2 or less. Otherwise, CC indicates you have metabolized free chlorine--ie there's something you are fighting. Since FC is .5 also, this is clear.
PH = 7.0 Normal pH range is from 7.2-7.8. For vinyl pools, anything below 6.9 is cause for concern. But with gunite, it's no big deal. In fact, I would leave your pH at 7.0 because chlorine is more effective at lower pHs than at higher ones. You can raise pH to more comfortable levels later when your chlorine holds.
TA = 100 Not to worry. For now, it's no issue. In fact, it should never be an issue at 100, but sometimes it is. However, I see no evidence of that. With gunite, though, never let it get past 120-125.
CH = 300 This is right in the middle of the recommended range for hard-sided pools like gunite--200-400 is the recommended range. Don't change it.
CYA = 60 This is where I have a problem. If you just emptied and refilled your pool, how did you get a CYA at this level? It just doesn't make sense because it shouldn't be in your fill water. I can only guess at 3 reasonable possibilities:
1) You need to re-run the test as you ran it incorrectly.
2) You've added CYA by either adding it directly, or by use of Tri-Chlor Tablets or Di-Chlor powder.
3) There was a lot of water left in the pool when you drained and the CYA had been insanely high before, and this is the residue of that.


But let's assume for now the number is OK. We'll go from there. A CYA level of 60 should use a shock level of 20ppm, not 24(?). But to get there, you'll need to use the same method we recommend for fighting algae, as you are fighting SOMETHING that's using all your chlorine.

Each gallon of 6% bleach will add about 3.5ppm of FC to your water. That means 5 3/4 gallons of 6% to get from 0 to 20ppm. (or half that of 12% liquid chlorine "LC"). What you need to do is add that much bleach to get your FC to 20. You'll have to check FC and add bleach/LC 3 times a day until your water holds the chlorine. If you've added it in the morning on a sunny day you WILL lose some to UV breakdown, but it shouldn't drop 15 points. Yeah, it's going to take that much chlorine until you kill whatever it is that's in your water.

If your water isn't clear, you should also vacuum to waste once a day, brush your walls once a day and back wash whenever the pressure rises.

But re-check that CYA test, please.

Good luck!

Carl