5-7 letters begins with a_a--
It's not exactly a yucca, though it is commonly mistaken for one, I think the word you are looking for is agave.
I'm wondering how I go about separating the agave plant?
This is easy. Just gently pull of cut the pups from the mother plant, making sure there are a few roots with it and replant. Since agave plants are similar in nature (and often mistaken for) yuccas, their care and separation is also pretty much the same. Therefore, this article for separating yuccas should help: https://www.gardeningknowhow.com/ornamental/foliage/yucca/separating-and-repotting-yucca-offshoot-pups.htm
How do you trim dead ends or leaves from an agave plant?
You can remove the leaves or any part of the plant that is dead, just make sure not to damage the trunk, branches or healthy pups. Since these plants are closely related to yucca plants, this article on pruning may be helpful as well: https://www.gardeningknowhow.com/ornamental/foliage/yucca/yucca-plants-care-and-pruning-tips-for-pruning-a-yucca.htm
I have a plant that I have not been able to identify and I haven't seen it in any books. It has spiky leaves and they are kinda inside each other and they stick out on long branches. There are only two branches to this. It has spotty leaves and there are tiny points on the end and the leaves are triangular shaped. All I know is that it is a succulent. I also would like to know the care of this plant.
Planting new Jeweled agave plants. How large does a Jeweled agave grow? How much space to allow between plants?
These articles will provide answers to your questions about agave:
Two of our agave plants have something on some of the stems.
It appears similar to images that show damage from the Caulotops barberi insect.
See the link below for information and treatment recommendations.
I have a pretty large Century plant that the majority of the "leaves" have flopped over. I have watered it a couple of times this spring thinking it might need water, but that didn't help. Just curious what I can do to get the "leaves" to stand up again.
Well, this is a bit puzzling since most 'floppiness' of the leaves is normally related to water stress. Of course, there is supposedly a particular variety of agave that flops naturally, though I think you would know if you had this type. With a little poking around, I did find another possibility, though it would likely be in a desert-like climate to be the case. An insect pest - agave snout weevil - can actually cause this to happen. Here is more information: https://www.gardeningknowhow.com/ornamental/cacti-succulents/agave/agave-snout-weevil-control.htm
I would certainly check the roots or crown of the plant for signs of rot, whether from too much water or a pest. Here is more information: https://www.gardeningknowhow.com/plant-problems/disease/root-rot-in-garden-plants.htm