4 weeks into a sprained ankle, still swollen, can walk with a limp, some pain. i can bare some weight but no great improvement. is this normal?

Ankle sprain : I would say ankle sprains are drastically under treated. You are 4 weeks post injury still with pain and swelling. This cn lead to functional instability see your local podiatrist asap.

Unstable ankle....: No it is not normal, especially after four weeks, unless your ankle has more than just a sprain. Swelling is a sign of instability and means that the more healing is needed. It's time for a re-evaluation of the ankle.