What's your question? Ask

It sounds like you have some drainage issues, which may be causing the lawn to become soft. You can regrade the yard some by adding thin layers of topsoil over the grass in the trouble areas and around the house, sloping slightly so that water/rain runs away. You will probably have to do it a few times, but just add a thin layer of topsoil, not enough to completely cover the grass but enough to bury the grass about half way up the blade. Once the grass has re-established at the higher level, do it again until the drainage issues are gone.

While I cannot be totally sure, the white dust you mention sounds like powdery mildew. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

This article should help: https://www.gardeningknowhow.com/lawn-care/lgen/eliminate-mushrooms-in-your-lawn.htm

I think it may be a form of Mullein. The most common variety is common mullein or great mullein and this is not that. There are about 250 varieties of this plant and yours has the characteristics of the family. It was likely a decorative variety of mullein that escaped from a garden.

You should be able to treat it the same as common mullein though. http://www.unce.unr.edu/publications/files/nr/other/eb9801.pdf

Roundup breaks down in a few weeks, so it should no be the problem. There are a few things that can cause this. One would be poor fertility in the soil. If you did not amend the soil, I would recommend that.you do that.

This has been a very rainy spring for much of the US. If this has been the case where you live, the seeds may have rotted in the ground. If you suspect this, wait until the soil dries some before planting.

Birds are also a factor. If you did not cover the seeds, they may have been eaten.

Too little water can also cause seeds to fail to germinate. You may need to increase watering.

The best way to be rid of them is to treat the area with a fungicide. The two most popular are Bayleton and Daconil. In addition to fungicide, which usually require repeat applications, you could try spraying them with a solution of baking soda (2 tbsp) and water (1 gal). This article should also help: https://www.gardeningknowhow.com/lawn-care/lgen/eliminate-mushrooms-in-your-lawn.htm