You have a bit of a learning curve ahead of you, but it all falls into place fairly quickly and becomes a simple routine before you know it. You can get a ballpark level for CYA by doing a diluted test. See point #9 in:
Pool School - CYA
CH at 975 ppm is manageable with other adjustments. But more importantly, the high CYA needs to be reduced, so a partial drain and refill is a good recommendation.
Depending on how sensitive you are to costs, you might want to learn your water cost and best timing for doing that. A call to your water company should help you answer that. Utilities in some places determine sewer charges for the upcoming year based on water use in winter, assuming you're not watering plants during winter. You could also get a quote for reverse osmosis which runs your water through a machine that removes CH and CYA from the water. This process also consumes water, but less than a partial drain/refill if good equipment is used. It might be more expensive than simply buying the water and paying any quota penalties.
There are experts here that might be able to comment on the plaster, but they'll likely want to see pictures and hear a description of how the plaster feels to you.
Your water is capable of depositing hard calcium scale on the plaster right now, so if it was my pool, I'd be using muriatic acid to lower the pH to 7.4 and try to hold it there while you're deciding how and when to proceed. The lower pH will offset the effect of the high TA and CH, and reduce or eliminate the risk of calcium scale forming on the pool surfaces. The cold water is helping right now, but as it warms the risk increases, and the risk is already high.
Cold water is also helping prevent algae, but 1 ppm FC is seriously too low. If it was mine, I'd raise FC to 10 ppm as soon as possible. Judging by the picture, two 1-gallon jugs of bleach would not be out of line in your pool (8.25% sodium hypochlorite, not splashless, not scented). But before you do that, and this is the only time we'll suggest a pool store, take a water sample and ask them to test for iron and copper and let us know what you find out. Taking a bottle to each of two pool stores is even better. If iron and copper are zero, you can add the bleach right away. Don't buy any chemicals they try to talk you into while you're there. With it being winter, you might need as little as a quart of bleach every few days to hold your FC up.
A signature on your posts will really help you get the best possible advice here. Click the link 'read before posting' in my signature to see the instructions for setting this up. Just put in whatever you know and you can update it as you learn the pool.
