First I would always follow the PB's instructions. If there is a problem you dont want to be the cause.

Second, there is much debate about the heating thing. We pebble pools on 110 degree days, and with the sun shining on the surface it is probably hotter then that, so will water heated to 100-104 hurt that, probably not.

Generally the colors get a little darker, then lighter with hydration.

You will get a cover pump with your cover. You can not move the cover with water on top of it, so it has to be pumped off. You can leave it open during a hard rain, but you will probably get a lot of debries in the pool from all of those trees. You want to be very careful if you do leave it open during a rain storm, as the first fold in the cover can catch a lot of water, so when you try to move it it is too heavy, and will tear the cover, or break the rope, or damage something. So generally best to keep it shut, and pump it off.
Talk to your PB about these things as well.