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A raised bed is certainly helpful, but you may still need to treat the remaining yard as well. These articles should help: https://www.gardeningknowhow.com/special/urban/raised-beds-for-urban-settings-no-digging-required.htm, https://www.gardeningknowhow.com/plant-problems/pests/lawn-grubs-how-to-get-rid-of-grub-worms.htm

Yes, you can use black plastic but this could cause drainage and aeration issues. I would recommend using something in the bottom that allows air (and water) to pass through, such as landscape fabric or moist newspaper. You can then put your compost/soil over top. The newspaper will eventually break down and further add nutrients to the soil. Here is additional infomration that should help: https://www.gardeningknowhow.com/special/urban/raised-beds-for-urban-settings-no-digging-required.htm, https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lasagna-gardening.htm

I would determine exactly how much space would be affected by the renovation and use the remaining area for a small garden. No sense in having it go to waste. That said, if you feel the renovation would endanger any plantings you have, containers or a raised bed elsewhere might be the way to go. This really depends on what you will be planting (i.e. vegetables - tender or hardy - flowers, etc.) Generally, a vegetable garden put in now would be finished for the season by next spring, when a new garden would be implemented, so you could use that space for your garden this season and then use whatever is left or containers for the following season.

You can actually go ahead and till the grass, provided it has not seeded. Then you could either treat the area after tilling with Round-up 2-3 weeks before planting the garden, or you could lay down some type of barrier, like landscape fabric or newspaper, to keep weeds out.

In more rural areas, planting in rows was easier as far as maintenance, watering, etc. since most plantations in the South were quite large. Limited space and more urban areas have little need for the traditional rows you are accustomed to seeing. That being said, the layout and planting of your vegetable garden is based more on personal preference and what works best for you rather than any specific order or design. However, planting crops in a way in which all are supplied with ample amounts of sunlight is best--such as with taller plants in rows further back to prevent shading. This article provides some layout suggestions that may help: https://www.gardeningknowhow.com/edible/vegetables/vgen/the-layout-of-your-vegetable-garden.htm

Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/plant-problems/weeds/how-to-kill-grass-naturally-kill-unwanted-grass-in-your-yard.htm, https://www.gardeningknowhow.com/special/urban/raised-beds-for-urban-settings-no-digging-required.htm, https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lasagna-gardening.htm