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If your grass is not making plumes, it is likely either too much nitrogen or too little phosphorous. This is caused typically by ornamental grass that is planted close to a lawn that is well fertilized. Lawn fertilizer is is high in nitrogen, which inhibits flower (or for ornamental grass - plume) development.

Both sides, either too much nitrogen or too little phosphorous, can be corrected with some high phosphorous fertilizer for the plant. Bone meal is a good fertilizer in this case. Try adding some to the plant and that should correct it.

Once you cut the plant back to the ground, you'll need to dig up as much of the root system as possible using a shovel, pick axe, etc. Be sure to discard these in trash bags or burn (if in a suitable location and it's safe to do so). Then apply a glyphosate herbicide (like Roundup) to the freshly dug area as well as to any plants that may pop back up. It may take several applications to fully eradicate the plant but with vigilence and patience, you will eventually win the battle.

Pampas grass is actually quite hardy and will survive mild winters such as this, so go ahead and plant the grass outdoors. For growing info and care, this article will help: https://www.gardeningknowhow.com/ornamental/foliage/pampas-grass/growing-pampas-grass.htm

You won't be able to tell what you have until it begins developing plumes (flowers). However, if this was purchased from a reputable nursery, the label should list its sex. Normally, females are the most commonly grown in home landscapes. They are much showier than their male counterparts with fuller plumes of silk-like hairs, of which the males do not have.

This article should help: https://www.gardeningknowhow.com/ornamental/foliage/ornamental-grass/no-plumes-on-ornamental-grass.htm

Sometimes grass needs 2-4 years to mature to blooming size, especially if the plants were seed propagated. Also, if growing conditions are 'perfect', the plants might be making an unrestrained root system. Many plants bloom when they are in less than perfect conditions because they feel "threatened", and will try to insure survival of the fittest. Both male and female pampas grass bloom.