Other than replacing all the soil, you can't exactly "remove" them. However, you can neutralize a lot of their impact by incorporating a healthy amount of compost into the soil. Compost is frequently used for bioremediation of contaminated soil.

You might want to consider having a soil test done to determine if there are specific chemicals or pesticides in your soil that you need to be aware of but I doubt you should have any significant concerns. And you need to be aware that testing for chemical contaminates requires that you supply exactly what contaminates you want them to check for, so check with your lawn service about what they might have applied.

Depends a lot on the toxin. Latex paint isn't toxic. As to lawn chemicals, pre-and post-emergent herbicides degrade naturally in a season, so at least there won't be a lot of remaining toxicity to plants. Lawn care people are pretty well-regulated these days on what they can spray on people's lawns. You're going to get as much inside you from being out on the lawn as you would from eating vegetables grown in that soil.

For peace of mind have your soil tested. Suggest you first contact the testing company and describe your concerns. They'll help you decide which tests are appropriate, and how to obtain good soil samples. Since you're testing anyway, have them report your soil's ph and if it could benefit from any specific additives.

Agree that having the house painted shouldn't pose any threat. It is more the herbicide lawn applications that would concern me when it comes to growing vegetables there. That and the problems created by growing right next to any structure.

"Also, can you grow winter vegetables in the shade? I live in North GA."

As a very general rule, no. Shade gardening even in summer can be difficult and is basically limited to some leafy greens. But there is even less sun exposure in the winter even in GA. So it all depends on exactly how much sun they can get in the winter when the sun is so much lower on the horizon and how much that little exposure is blocked by surrounding structures and trees.

Dave