ummm.... I'm not seeing any attachment
Part of what you are talking about is more like succession planting than companion planting. Succession planting is one after the other (even if they overlap a bit). Companion planting is planting things next to each other at the same time.
Carrots and tomatoes are kind of both. The carrot seeds get planted much earlier than the tomato transplants go in the ground. But carrots take a long time, so they will still be growing for a good while after the tomatoes are planted. But they work well together ("Carrots Love Tomatoes" is the title of a well known companion planting book). So I usually plant a row of carrot seed down the outside edges of beds that tomatoes will be planted in later.
In between rows of tomatoes, will be a very shady spot once the tomato plants are getting big. And you need to be able to get to your tomato plants to harvest and tend, so you don't want to fill the space too much. Four rows of tomatoes in ten feet is fairly close spacing. Once the tomatoes are going well, there's not going to be much in between. That's why I just put the carrots on the outside edges, where they can still get some sun. But if you really want to put something in there, think about lettuce, spinach, etc. They get planted early and done quickly, so they will be out of the way sooner. When the weather has warmed up, the lettuce will benefit from the shade and maybe be a bit slower to bolt.
You have watermelons in the same 10 by 10 as all this? I don't think so. Have you grown watermelons before? The plants are huge and voracious consumers of nutrients and water. I think the only way that will work is if there is lawn around your 10x10, so that the watermelons can grow OUT of the bed across the lawn, not into the bed. And even so, you will have to work really hard at keeping everything, fed, watered, mulched, etc to make up for what the watermelon uses. And yes, if you have carrots there, the watermelons will just completely overtake them.
Another succession planting I use if I don't have carrots on the outside edges is to plant broccoli there. I start my broccoli from seed indoors, very early and plant it in the ground a month BEFORE my average last frost date (broccoli is very cold hardy and frost tolerant once hardened off). Then once all danger of frost is past, I plant tomatoes behind them. By the time the tomato plants are getting big, the broccoli is about done and can be pulled.