Will weeds get them or will grass take over? It all depends on your attitude toward your garden. A lot of your questions that you asked can only be answered by actually doing it and see the outcome for yourself. No one could really tell you what's gonna happen if you do or don't do something because they don't live next door to you and see you through every steps of the way. No easy way around, over, or under it. Do it, and accumulate experience along the mistakes(they are inevitable). Wish you have a successful vege growing experience. And please come here often and share your joy of gardening (preferably AFTER doing your best for it, not BEFORE)

is it possible to just flip some rows of soil in my back yard which is flat and low grassed, then add soil?

Possible? Sure. Common practice? No. Recommended? No. Limited possibilities of success for lots of reasons if done that way and successful production is the ultimate goal, right?

But many folks like to experiment so as already mentioned you will learn a lot about what not to do next year in the process.

Dave

I started a garden once by removing the sod, then adding compost to the soil underneath. It wasn't the best, it wasn't the worst. Whether or not weeds take over will be determined by your diligence in removing them. Preferably when they are small. Or if you choose to use mulch once your seeds are up. Now grasses taking over, that could be a real struggle depending on the type of grass. If it is a bermuda grass lawn... You have your work cut out for you. You could potentially interplant your radish and arugala with your tomatoes, harvesting the arugala and radish as the tomato plants get large. Just some ideas. Cheers!

It could depend on what type grass you are talking about. Here in Texas the grass has to be killed before any plantings as our grass [Bermuda) will overtake almost anything it can. When I was up in Indiana some of the farmers there have gone to spraying roundup at the same time as planting the seed crop.

You might want to do some research into what are called Lasagna Garden beds - multiple layers of materials just built on top of existing ground. Lots of info about them on the web. Just Google 'lasagna gardening'.

Dave

I was going to suggest interplanting too. You can also grow your peppers in pots if you want. If you clear out your dead cucumbers , you can plant there too.

is it possible to just flip some rows of soil in my back yard which is flat and low grassed, then add soil? NO.

It would be best if you shoveled the sod off the patch. Those grasses have tendency to regenerate if you don't remove them.

For seeds to plant, look up a planting schedule for your area. Below is one of them. Since you live in a warmer part of the country, you can garden year around.

Here is a link that might be useful: Florida vegetable planting Calendar