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I assume you are asking about liriope, or Monkey Grass. This article should help: https://www.gardeningknowhow.com/ornamental/groundcover/monkey-grass/monkey-grass-a-spectacular-groundcover-for-the-lawn.htm

Liriope should be cut back annually. The best time is just before it starts new growth in the spring. For zone 6b, we usually cut ours to leave about 4''. If you think your clumps are too large, fall is an ideal time to divide and replant. Depending on the size, you could get as few as 2 or dozens of clumps to replant. We usually divide into clumps of 3-5 crowns for a 4'' pot, or 8-10 for a 1 gallon pot.

This is simply a propagation term used by commercial growers in the trade. Nurseries will divide the crowns of plants, like liriope, and then trim the leaves and roots to make a single plantlet, which they refer to as a 'bib.' So when you hear them say a pot contains 4 bibs, they are simply saying there are 4 little plantlets in the pot.

Liriope (similar to monkey grass) is normally cut back in early spring, just as new growth begins. This article will help, as it applies to liriope as well as monkey grass: https://www.gardeningknowhow.com/ornamental/groundcover/monkey-grass/pruning-monkey-grass.htm The best rule of thumb on pruning lilacs is to do it right after the flowers die off in the summer. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/shrubs/lilac/pruning-lilac-bushes-when-to-trim-lilac-bushes.htm

You have several options: I would recommend pouring boiling water on the areas where the bermuda grass was growing. Boiling water will kill whatever it comes in contact with. Alternatively, you could cover liriope clumps with cardboard boxes or use a gallon milk jug with the bottom cut off as a shield. Spray the grass with an herbicide during hot weather when the grass is actively growing. One application won't work, as it's going to take several. If a little herbicide touches the liriope, don't despair. It will only kill the little sprout, not the clump. Ortho Grass-B-Gon will kill grass and weeds but won't harm your liriope.

You can cut the liriope (monkey grass) back to 3 inches in early spring. After trimming, you can fertilize and implement weed control as well. Then, mulch the area with straw, bark or compost.

For more information on pruning liriope please visit the following link:
https://www.gardeningknowhow.com/ornamental/groundcover/monkey-grass/pruning-monkey-grass.htm

The water oaks in a way are draining the life of the things around them. They are very water hungry trees and they literally suck the water out of the soil around them so it can make it hard for nearby plants to survive if there is not enough water for both the tree and the plants.

The container may work, but you would need to provide extra water for the liriope in the container. The container wall will prevent the trees from taking their water but it also means that the liriope's roots will not be able to grow outward to find additional water.