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I would be afraid to use anything without causing harm to the Dymondia as well. If the problem is not more than hand picking can do then this will be the most effective method. You can try spraying vinegar directly onto the pest plants, but you will want to be very careful not to spray too much onto the lawn.

This plant will usually outcompete pest plants, over time. Some things are still aggressive though. This article will help you with the care of this lawn: https://www.gardeningknowhow.com/ornamental/groundcover/dymondia-groundcover/planting-dymondia.htm

Do a Google search for seeds. You can also plant with plugs.
This article will help you.

https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/dymondia/dymondia-as-grass-substitute.htm

I think that your measurements are about as accurate as it gets. They will fill in within the first season, and certainly by the second.

This article will help you.
https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/dymondia/dymondia-as-grass-substitute.htm

We do not sell, or recommend places to purchase. You could try vendors on Amazon, Etsy, or Ebay, though.

Deep watering will be different from area to area, and very dependent on soil composition.

This will be a learning game until you hone in on the needs of your lawn, but generally you will water until you notice runoff. This can be 30 minutes, or it can be a couple of hours. This just depends on your soil and local conditions.

Here is an article that will help you to determine how much you should water your lawn:

https://www.gardeningknowhow.com/lawn-care/lgen/lawn-watering-guidelines.htm