Hello, to get wheat, you need to use your scythe on grass to get some seed and use your shovel on sand to prepare the ground. Once the ground prepared, you can plant the seed (use seed on prepared ground) and if you wait a bit until the plant become yellow, you can then use your scythe to harvest the plant, giving you wheat. It's useful to make healing bread.
For the map, you can finish the game without it, but it's useful so that you doesn't get lost, and also to find the entrance to the cave. There is also 4 red locations on the map that you can go dig to find something that could help you against the final boss.
Have fun with the game!