I would get the winter squash in the ground right now.

I would be inclined to start the others inside. I started many fall plants on my front porch with the perfect combination of sun and shade. Everything germinated well but some bugs found them and began eating them (probably flea beetles). I covered it with row cover fabric but that just trapped the bugs and now I will be starting the next round indoors.

If you have a cooler season of fall that's when you'll want to transplant them. Might be info on a regional gardening forum for you. Direct sow the carrots & start the others with the kit. No neat mat necessary in your climate.

Cool season vegetables survive frost and some even hard freezes, so you should be able to harvest throughout the winter. My 1st frost is mid-Oct & since I'm also in northern USA most fall crops are planted by mid July to mature enough to hold through winter. Spinach and lettuces can be planted until mid Sept.

Some vegetables are easier. Kale & lettuces are great 1st plants as are the onion/garlic bulbs. The others a bit more tricky, but very doable.

I agree with Tish about starting the winter squash now. Despite the name it is a summer crop. It will die with the first frost. Given your zone you could probably do 2 winter squash crops per year. Start one inside a couple weeks before the last frost date and the second about now.