Ah Frostfall, a wonderful mod.

Pretty harsh though. What setting do you prefer? I have the game on Lite, but then I dumb the exposure rate way down to 0.3x I think. So it's possible for my characters to freeze to death, but this takes a good while to happen.
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For the first issue, go into the MCM menu and then look in the Effects & Interface menu. Hopefully you have the same version of Frostfall that I do. If you don't see this menu, maybe it's called something else.
Anyway, go into the menu which deals with all the onscreen-menu stuff. There should be a section called Visual Effects, another called Meters, General, etc. In the Meters, General section, make sure Meter Display is "Always On", and not Contextual. Contextual menus only show if there's some sort of large change in temperature going on.
Go down to the Indicators menu, and make sure Weatehrsense Gem Display is also Always On.
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Question 2: I have no idea. I assume you're using the WEAR feature? I think that is what you're talking about here. I don't use WEAR so not sure.
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Be careful removing mods!!!!! ... Sometimes when you remove a mod, its script will still be in the Data folder and this can mess things up. Which mod manager are you using? If you're using Wrye Bash, you're okay. Bash will automatically remove scripts, and anything else associated with those mods.
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Now I hadn't had these issues until I installed this patch, so I'm thinking I need to roll back to a save before enabling Frostfall and uninstall everything and reinstall Frostfall, Campfire and Papyrus and get rid of the patch.
This sounds like a good idea!