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Now that the plants have been in for a month, switch to watering less frequently while make sure the soil is moistened more deeply. This will make sure the plants' roots are encouraged to grow deeper into the soil. After watering, simply push your finger into the soil to make sure the soil is moistened several inches down. You can reduce watering to every other day, then once a week. You can reduce the water the plants get if it rains, and increase it if they start looking wilted. See this article for more:

https://www.gardeningknowhow.com/garden-how-to/watering/watering-garden.htm

Dymondia should be fertilized once each spring with an all purpose grass fertilizer. Here is an article with more information: https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/dymondia/dymondia-as-grass-substitute.htm

Many people don't need to trim their dymondia at all. If yours grows too tall, a lawnmower would probably work more evenly than a weed whacker.

This plant will benefit, substantially, from dividing when it gets over-crowded. What you will want to do is dig up as much as possible, shaking the dirt out. Split them up by pulling them apart from one another. Plant half back in to the original area and the other half wherever else you want them. Make sure to water-in everywhere you plant to set the roots back in the soil properly.

This can be a tricky subject, but this website provides a good answer for this: https://www.houzz.com/discussions/2159928/how-to-stop-grass-weeds-from-growing-while-dymondia-taking-root

As long as it is just partial shade, it should be fine. They really prefer full sun. Here is an article that will help: https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/dymondia/dymondia-as-grass-substitute.htm