Good for you Brina! I am sure you will reach your goal without a problem!
I know it sounds strange but maybe you could accomplish your second goal better by setting the first one aside. I find that I run faster overall when I take walking breaks every kilometer of running or so. Or when I do Fartleks (or intervals), pushing to my max and then slowing down and then to my max again. And I mean _significantly_ faster, like shaving 3-4 minutes off a usually 30-minute 5k.
Also, what Lise said about bricks: it's really important to at least try it a few times, cycling and then going for a short run. When the day of the race comes, you won't be surprised that your legs feel awful for the first few minutes of running, and you'll know that this awful feeling is going to go away shortly. So you won't get discouraged and run happily to the finish!
Starting to run after a long period of non-running is a big challenge! Good luck, I'm sure you'll do wonderfully!