What's your question? Ask

This is generally a fungus mold and may be due to soil that is not sterilized.

Make sure you use a good quality potting soil for container plantings.

You also can have fungus and mold issues if the plant does not receive good air circulation and or too much moisture.

Most types of fungus like this will not kill the plant, but you can make sure it does not spread or continue.

Increase the light and even place a small fan in the area.

You may want to consider a ground cover that may do better then grass under a large shade tree.

https://www.gardeningknowhow.com/ornamental/trees/tgen/tips-for-growing-grass-under-a-tree.htm
https://www.gardeningknowhow.com/ornamental/groundcover/gcgen/ground-covers-under-trees.htm
https://www.gardeningknowhow.com/special/shade/ground-covers-for-shade.htm

Personally I would say Kentucky Bluegrass, or any fine Fescue. These would be suited just fine for your area.h

This can be done, as long as you can replicate its native environment. This article will help you on their care: https://www.gardeningknowhow.com/ornamental/water-plants/cordgrass/cordgrass-plant-growing.htm

Here is some more useful information on the subject: http://planttalk.colostate.edu/topics/annuals-perennials/1023-water-gardening-containers/

I would allow at least a week to let it break down a bit. I would recommend fertilizing after the grass has established. Too rich of a soil at germination can burn young seedlings.

This website seems to offer some information on this subject: https://www.todayshomeowner.com/best-drought-tolerant-lawn-grass-for-sandy-soil/