Over a period of 12 weeks, your longest run will increase from 3 to 10 miles. Don't worry about making the final jump from 10 miles in practice to 13.1 miles in the race. Inspiration will carry you to the finish line, particularly if you taper the final week. The schedule below suggests doing your long runs on Saturdays, but you can do them Sundays, or any other convenient day, as long as you are consistent. It could be walking, or biking or swimming, or some combination of all three mainly to relax your muscles before or after your long runs.
Strength training is another cross-training option.
Generally, I recommend that runners use relatively light weights and high repetitions. If you already lift, you can continue to do so as per your regular schedule, but it's usually not a good idea to lift before you run. After, or on another day of the week, usually works better. Repeat the week you just completed before moving up to the next level. You will be able to use your times to predict your finishing time in the half marathon, and what pace to run that race.