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It looks like clover with heart shaped leaves, instead of rounded. (They taste like green grapes, and are edible as long as you don't go eating a pound of it at a time)

This article will help you to control these invasive weeds: https://www.gardeningknowhow.com/plant-problems/weeds/managing-oxalis-weeds-in-lawn.htm

Yes, I would definitely wait to plant these. The plant will stay in hiding from the summer heat, but will be better suited for Fall or Spring plantings. I recommend Spring plantings over Fall, but they will usually do fine if planted in early fall. (Hard to say when Fall will come and stick around with Tennessee weather isn't it?)

This article will help you with the general care of oxalis: https://www.gardeningknowhow.com/houseplants/shamrock/caring-oxalis-plants-outside.htm

They go dormant in winter, or even as early as late summer in hot areas. They need a period of dormancy where it is mostly dry (only a few drops of water per week) and cooler. Darkness helps to keep it from sprouting at inopportune times.

Without a dormancy each year, they will start to lose vigor and slowly die off completely. This article will help you to know how long the dormancy should last, and how to care for the plant: https://www.gardeningknowhow.com/houseplants/shamrock/growing-shamrock-plants.htm

It sounds like oxalis. If so, this article should help:

https://www.gardeningknowhow.com/plant-problems/weeds/managing-oxalis-weeds-in-lawn.htm

Boiling water should kill it but may not get all of the rhizomes, only the top growth. When using a selective herbicide, which won't harm the lawn, take care to avoid any ornamentals. This article explains your options:
https://www.gardeningknowhow.com/plant-problems/weeds/managing-oxalis-weeds-in-lawn.htm

This is only hardy down to zone 7, so it will only be considered an annual in your area, outdoors. You should plant these in Spring, after all threat of frost has passed. You may want to dig some up before each winter if you would like to keep it around. It will die out completely in winter in your area.

This article will help you with their care: https://www.gardeningknowhow.com/ornamental/flowers/candy-cane-oxalis/growing-candy-cane-oxalis.htm