Does an ankle brace protect the ligaments in the ankle?

OTC Ankle brace. You're better off using an otc brace or splint that trying to tape yourself up at home. It's not as easy as the professional trainers make it look. You could also just see a podiatrist - many of us stock simple braces for simple sprains. These will protect the ligaments of the ankle - that's what they are designed for.
Yes. Ankle bracing has been shown to be effective in reducing the incidence of recurrent ankle sprains. Properly used, they are more effective than taping; but, proper strengthening, conditioning, and proprioceptive training is the most effective means of injury prevention.
Brace. It depends on the type of brace as there are many as well as what ligaments you are referring to. An exam and discussion with a podiatrist is your best answer.