Answer: Unfortunately, most vegetables require full sun or sun for at least six hours a day, so you might be very limited in that regard. Greens such as lettuce and spinach might tolerate the low light, as might some of the herbs such as parsley and basil and mint. Instead, you might want to consider a garden using shade loving perennials such as hostas, ferns, astilbes and violas along with bleeding heart, pulmonaria and lily of the valley. Perhaps too some annuals such as impatiens and even some bulbs such as caladiums for all season color. Burpee offers a wide selection of plants suitable to shade (Call Burpee at 800-888-1447 to order a catalog.)
In my experience the best way to cope with wild animals who want to eat your plants or dig amongst them is to put up a fence; there are many "folk" remedies and methods but a fence is the most effective over time. You might be able to use a picket fence or one made out of rough wood to match your rustic setting (or any design you like) and line that with wire mesh for the best barrier.
Q&A Library Searching Tips