The black plastic won't cause mold or fungal disease. But it will stop air and water from penetrating your soil. If you use the black plastic, you will have to be very conscientious about watering. Also, the black plastic may heat up the soil, even to the point of burning the roots of some plants.
If you want a weed barrier, landscape fabric is a better choice. It prevents light from getting through but allows water and air to penetrate. As to the size of the hole for the plants, I'd cut the hole about 4 to 6 inches away from the base of the plant.
