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While some would say fall planting is desirable, I would suggest waiting until spring to plant this warm-season grass. Generally, sprigs and sod will not produce roots unless the soil temperature exceeds 55 degrees F. for several weeks.

Here are some links that will help you with your new lawn.

https://www.gardeningknowhow.com/lawn-care/specific/centipede-grass/centipede-grass-care-planting.htm
http://edis.ifas.ufl.edu/lh009

I have read through the fact sheet on Paraquat and I believe there is enough information on there to say Centipede Grass may be dead if it was hit directly with this herbicide spray. If it was more of an overspray, your grass may have more of a chance.

Here is the information I found.

https://www.gardeningknowhow.com/lawn-care/specific/centipede-grass/centipede-grass-care-planting.htm

Aerating a Centipede lawn is recommend in early summer; during active growth of the grass.

If you soil is very compacted you can aerate twice a summer.

https://www.gardeningknowhow.com/lawn-care/specific/centipede-grass/centipede-grass-care-planting.htm

Epsom salt is Magnesium sulfate. The only reason you should use it alone as a fertilizer is if a soil test has shown your soil to be deficient in Magnesium and Sulfur. If you are just guessing, then you could throw the mineral balance off and cause problems. And yes, MgSO4 can burn if used in excess, but not likely if it is prescribed in a blend of recommended fertilizer products to correct known deficiencies.

Soil analysis and Rx mineral amendments is the best way to go. But most people use general purpose lawn fertilizer that is rich in Nitrogen, Phosphorus and Potassim (NPK) and other nutrients, of which Magnesium can be one. The more complete and scientifically balanced the better.
But to use Epsom salts alone just because you have some may not be a good idea.

The best control is achieved by using a weed control product that contains glyphosate. Now would be the best time to spray to control Centipede. Unfortunately, glyphosate is a non selective weed control and will kill both the desired and undesired grasses. Therefore, the area will need to be reseeded. I will state that there is a possibility that some of the Centipede will survive and start growing again in the spring. Although it is not as effective, a broadleaf weed control that contains 2, 4-D will damage or even kill Centipede grass. It is best applied in late spring/early summer when the Centipede breaks dormancy and starts growing again.