Question re Mulch and a St. Augustine Grass question.

I planted impatients along my walk way this spring and I used cypress mulch around the plants. As the plants die back this winter, I planned to till them under. Is it ok to till them mulch into the soil or should I remove it before tilling?
Next. I have a lawn that has a small area of centipede. The rest is mostly weeds. I have a few areas I "sterilized" and sprigged an unknown variety of St. Augustine. I have fertilized the St. Augustine, watered it well and often ( well drained soil ) and even talked to it, but for the most part my extra attention is for naught. Every few days I can look at the patches and there will be a few plants taller then everything else and growing very well - I pull these out because they are weeds, doing better then my lawn. Some of the St. Augustine has little dead spots on the leaves and looks pretty sad. The rest of the lawn (all weeds) are growing at a maximal rate. Any suggestions to help my grass? Also, there are 3 weeds that are bothering me: 1.) Crab grass - what is the best way to control this. I used IMAGE but was not all that impressed and it killed a large area of my centipede. 2.) Unknown weed: This weed has braid like roots. It will then send up long "Y" shaped stalks with black seeds(?) on the ends. I don't know what it is, but can I reasonable kill it? 3.) Unknown weed: This is a very thin stemmed weed that grows by colons and puts down roots at each joint. The blades are fine and thin. Grows very rapidly.
Thanks for any suggestions you can provide.
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