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No sugar will not kill weeds. You can use corn gluten in the early spring to help control crabgrass and other types of weeds. If the weeds are not in the middle of the lawn, horticultural vinegar will kill them. But it only kills the top growth, you can however, "wear out" the weeds by repeated application.

This article will help: https://www.gardeningknowhow.com/plant-problems/weeds/crabgrass-control.htm

The following link should answer some of your questions: http://www.scotts.com/smg/goprod/turf-builder-with-halts-crabgrass-preventer/prod100056/
You will find contact numbers at this site.
Always follow package directions.

You have several options:

I would recommend pouring boiling water on the areas where the crabgrass was growing. Boiling water will kill whatever it comes in contact with, but you'll have to protect the monkey grass.

Alternatively, you could cover monkey grass 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 monkey grass, don't despair. It will only kill the little sprout, not the clump.

Finally, you can use the old standby--hand pulling all the unwanted grass. If hand pulling is not viable, you can try using Ortho Weed-B-Gone. This will kill the crabgrass but not harm the monkey grass.

This article should help: https://www.gardeningknowhow.com/problems/weeds/crabgrass-control.htm

There is no easy answer to crabgrass!
This weed grows and invades and reseeds easily.
Using a herbicide in among your flowers and plants is very difficult without the risk of killing your established plants.
Pulling and weeding is the safest method.
I just spent 4 hours digging up a strawberry bed that was invaded by crabgrass!

You can try to smother the crabgrass with newspaper and some gardeners use hot water poured on the weed to kill.
The hot water method I find make it easier to pull up.

https://www.gardeningknowhow.com/plant-problems/weeds/crabgrass-control.htm