I always transplant basil to the same level as it was originally. Unlike tomatoes, it is actually a woody shrub, so of course, as the stems age, they'll harden up. It's only the new growth which is soft.

Yes it can take root. I Broke half a plant off at about 10 inches in length, and stuffed the broken end in wet soil. It wilted a bit, then took hold and did quite well, but took almost a month. Pepper plants can also be planted deeper too.

I have basil and parsley in large container outside. Should I bring them in for the winter?

Basil will definitely die if left outside in the winter. It even dies outside in winter here in California. Parsley, I'm not so sure about. Basil is considered an annual, so you might have to plan on planting some more in the spring. I've had parsley last 2 years before it got too woody and had to be replaced.

Here is a link that might be useful: What's Growing On?

Parsley survives my winters in the ground and I'm in Western NY State, but it is not really usable beyond the first year. It often dies/bolts early in the season of the second year. Use it up before the killing frosts and don't worry about bringing it indoors. Start with new parsley next year.

FataMorgana