What's your question? Ask

How long had it been neglected? If it wasn't too long a period, there is a chance that a good soaking will revive it (though right now it should be entering its dormancy period). Unless you live in a relatively warm climate, planting it outdoors 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.

I would give it some more time. Warm season grasses begin to grow much later in the spring.

For more information on fountain grass, please visit the following link:
https://www.gardeningknowhow.com/ornamental/foliage/fountain-grass/tips-for-care-of-fountain-grass.htm

Yes, you can - here is an article on how to use a tree stump as a planter:

https://www.gardeningknowhow.com/garden-how-to/projects/tree-stumps-planters.htm

This winter was particularly cold for most of the U.S. It is possible that it simply got too cold. Another possibility is that if the area it is growing is too wet, it cannot tolerate that over the winter. Here is an article to help you determine if it is dead or just on a slow start: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

They typically emerge in late spring to early summer, though with the unusual weather this past winter, the fountain grass may simply be slow to start. I would give it a little more time, and if necessary cut away any dead growth, which will help encourage new growth.