Broken Lateral Malleolus (left)

Hi all,
I was jogging on June 10th, rolled my ankle on a baseball sized rock. I was able to walk a mile, with a limp, back to my living quarters, with slight pain. My ankle was swollen and red. Bruising and more swelling ensued. I went to the doctor and was told I had a grade 2 sprain. No xrays were ordered. I continued walking with slight pain for the next several days. I felt that "something" just wasn't right with my ankle. Nine days after the incident, I went to another doctor. The second doctor ordered x rays. The x rays show a fracture. I'm now in a cast for 8 weeks. My photo is attached.

My questions:
Can this type of injury heal with the aid of an ankle brace instead of a hard cast?
If I have other damage (ligaments) will the cast assist with the healing?
Will this type of injury require physical therapy?

What am I looking at here as far as time, healing and getting back to my routine? I miss my daily running.

Thanks.