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It could be lawn grubs or a fungus of some kind. These articles should help: https://www.gardeningknowhow.com/plant-problems/pests/lawn-grubs-how-to-get-rid-of-grub-worms.htm, https://www.gardeningknowhow.com/lawn-care/lgen/grass-fungus.htm

It sounds like you have a fungus. You will need to treat the lawn with a fungicide. This article will help: https://www.gardeningknowhow.com/lawn-care/lgen/grass-fungus.htm

This article has good, basic advice on the approach to dealing with lawn grubs at any time of year.
https://www.gardeningknowhow.com/plant-problems/pests/insects/get-rid-of-grub-worms.htm

It sounds like a puffball mushroom. Here is more info on them:
https://en.wikipedia.org/wiki/Puffball

This article will help with keeping them from growing in your yard:
https://www.gardeningknowhow.com/lawn-care/lgen/eliminate-mushrooms-in-your-lawn.htm

Killing weeds in the lawn involves knowing first what kind of weeds you need to kill, because they don't all require the same kind of herbicide, or to be treated at the same time, and then you need to make sure the products you use are safe for the type of grass you have. It will require some research, using articles such as these: https://www.gardeningknowhow.com/plant-problems/weeds/
However, you can also rely on expert assistance from the folks at the county extension service. This link will help you find the nearest office:
https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm

We can't provide specific product or store names, but if you enter the question "where to buy St Augustine grass seed" into your browser, you should be able to find some sources. I must say that there doesn't seem to be much seed out there. While it may be technically possible, I suspect that it's not working as well as people would like. You might like to consult with the county extension service. This link will help you find the nearest office:
https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm