That doesn't look like a slug, because it looks like it has segments. I think it's a caterpillar. And that looks more like caterpillar excrement. But if it is an unusually marked slug, it will be slimy. Caterpillars are dry, and have legs. Whatever the case, good job finding it. Getting rid of it is easy and disgusting. You should pick it off (you don't have to use your skin if that bothers you), and kill it (squash, cut in half, etc). That may be the only one you have.
So, to answer your questions:
a) Why did this happen?
It is pest damage. You found the pest and control will be easy.
b) Should I still eat the lettuce?
Yes, you can. Make sure it is thoroughly washed first, but it is still edible.
c) How do I actually harvest Batavian lettuce?
You can harvest in whatever way is convenient. The most efficient way, total production wise, is to harvest on a regular basis, removing a few of the oldest leaves (the ones on the outside of the rosette) at each harvest. This keeps the plants productive, and the leaves fresh. Alternatively, you can wait until the plant has formed a somewhat denser head, and cut it off at soil level. This way, you'll get it all at once, and the plant may not grow back from the base, if you cut the stem.