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Most types of ornamental grass can be cut back in spring once new growth begins to emerge. Simply cut off the dead/old growth.

These articles may help:
https://www.gardeningknowhow.com/ornamental/foliage/ornamental-grass/sensational-borders-with-ornamental-grass.htm
https://www.gardeningknowhow.com/ornamental/foliage/fountain-grass/fountain-grass-pruning.htm
https://www.gardeningknowhow.com/ornamental/foliage/fountain-grass/tips-for-care-of-fountain-grass.htm

Yes, you can. It does well in containers. The growing requirements are the same as those planted in the ground, with exception to watering. They will require more watering, especially when temps are warmer.

This article will help you with that: https://www.gardeningknowhow.com/ornamental/foliage/fountain-grass/fountain-grass-pruning.htm

You can treat with a fungicide, but often ornamental grasses recover from this problem on their own. Just make sure that you cut it back this fall and that you discard the infected foliage in the trash.

Some ornamental grasses can become invasive because of their seed plumes, while others do not. You would be best researching the specific type of grass you have to see if it is an invasive variety. Regardless, you do not need to remove the plumes as soon as they appear. They are the flowers of the grass, and just like your other flowers, the seeds don't develop right off the bat. They will be fully developed when the plume starts to brown and dry out and this is the time you have to cut them off to keep the seeds from spreading.