Container gardening & compost?

I'm a newbie to container gardening. My family who has the in-ground type gardens tells me to throw ground up eggshells, coffee grinds, banana peels, etc. as "natural fertilizer" in my containers because they do that in their regular gardens. Considering that container gardening is somewhat different than regular gardening (e.g. soiless media seems better than regular garden soil since there is less disease, weeks, etc.) - is this natural food compost OK for container gardening? Or am I going to breed disease to the vegetables (tomatoes, cubers, etc.)