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This can be a difficult situation. You can try diotomacious earth, if you have not already. Pepper extract mixed in water can deter them some too, without harming your lawn. Sometimes boiling water can destroy large colonies, but it will not prevent them from coming back. This article will offer more solutions: https://www.gardeningknowhow.com/plant-problems/pests/insects/how-to-control-ants-in-lawns.htm

What will likely have to happen is that you will have to kill off that entire patch. You can do so without harming the soil and keeping the ability to plant immediately after by pouring boiling water directly on the spots. It will kill everything that it touches, but will leave the soil clean and ready to plant.

You can then take plugs from your existing lawn, and plant a patch that will take back over.

This could be caused by a large number of different things. This article will help you to start narrowing down what the cause could be: https://www.gardeningknowhow.com/lawn-care/lgen/lawn-and-garden-holes.htm

It would appear that fungicides aren't always effective. The best way to treat this is to provide conditions that the grass thrives in, but not the fungus. This article will give you more information: https://www.gardeningknowhow.com/lawn-care/lgen/pink-fungus-in-lawns.htm

This article will help you.

https://www.gardeningknowhow.com/lawn-care/lgen/treating-lawn-diseases.htm

These links will help you.

https://www.gardeningknowhow.com/lawn-care/lgen/grass-fungus.htm
https://www.gardeningknowhow.com/lawn-care/lgen/powdery-mildew-on-grass.htm
https://www.gardeningknowhow.com/lawn-care/lgen/eliminate-mushrooms-in-your-lawn.htm