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Yes, anything below 32 degrees F. is considered freezing. This article will help with covering the plants: https://www.gardeningknowhow.com/plant-problems/environmental/protect-plants-in-freeze.htm

It sounds like you may have a clay layer of soil under the topsoil. Heavy clay can act almost like a layer of plastic below the topsoil, not allowing any water to trickle down through the layers. Unfortunately, there are no really easy ways to correct this. One common practice is to build up the yard or improve its drainage. These articles will help with that: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/yard-drainage-problems.htm, https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/how-to-improve-clay-soil.htm, https://www.gardeningknowhow.com/special/spaces/creating-and-using-berms-in-the-landscape.htm Your other option is to learn to garden with it. There is a type of gardening style called rain gardens where people actually work to create conditions like what you have in your yard. It uses plants and trees that not only do well in those conditions but also help to suck up excess water. You may be able to turn your yard into a rain garden or even a bog. Otherwise, you could implement raised beds for gardening. Here is more information on those: https://www.gardeningknowhow.com/special/spaces/rain-garden-design.htm, https://www.gardeningknowhow.com/special/spaces/designing-bog-gardens.htm, https://www.gardeningknowhow.com/edible/vegetables/vgen/raised-vegetable-gardens.htm

It really depends on the plant and where it is located outside. If you are concerned about frost or cold damage, this article will help: https://www.gardeningknowhow.com/plant-problems/environmental/frost-how-to-protect-your-plants.htm

This article will help: https://www.gardeningknowhow.com/houseplants/hpgen/raise-humidity-for-houseplants.htm Outdoors, all you can really do is keep the plants misted daily unless in an enclosed area where the use of water-filled pebble trays would help.

Generally, you want to uncover your plants early in the morning, to avoid condensation under the covering. If your plants can't take temperatures of 40F, they're probably pretty tender, and will need more elaborate cold protection. Here are a couple of articles with ideas on cold protection: https://www.gardeningknowhow.com/plant-problems/environmental/protect-plants-in-freeze.htm
https://www.gardeningknowhow.com/plant-problems/environmental/protecting-plants-winter.htm

Somewhere along the line we lost the info about what "they" are. So, generally speaking, if you have a winter hardy plant, you can cut it back when it freezes, and cover with 4 or 5" of mulch - chopped dry leaves, straw, or pine boughs work well - as protection. If your plant was a tropical, it should have been brought inside for the winter; if the leaves have been hit by frost, you still have time to dig up the roots, put into a pot, and store in a darkish and cool place safe from freezing. If you can't bring it in, you can try cutting it back and mulching, and hope for the best. Some sub-tropicals can survive, some can't. If you can send us the name or names of the plant or plants you're wondering about, we may be able to give you better instructions.