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Are you sure what you have is truly fountain grass? I'm only asking because this grass rarely causes problems with taking over--they are not aggressive spreaders but rather clump-forming. At any rate, yes they can be pruned. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/foliage/fountain-grass/fountain-grass-pruning.htm

I would say yes, go ahead and prune it back but merely give it a good trim rather than a hard prune. Save that for late winter/early spring. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/foliage/fountain-grass/fountain-grass-pruning.htm

First of all, I would cut the plant back, removing all dead or dying growth. This should help rejuvenate the plant. Most likely the plant is in shock. This article sohuld help: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

Unless you live in a relatively warm climate, leaving it outdoors during winter will only kill it, as these plants are warm-season grasses and do not tolerate cold. In fact, in cooler climates, they are often treated as annuals or overwintered indoors. You could try watering the plant and leaving it be (indoors) over winter (watering once a month) and put it outdoors in spring to see what happens. Unfortunately, you might need to replace it in the event that it doesn't show signs of life.

Spring is the very best time to plant new plants, but early fall is a very near second. You will be fine if you plant now.

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