You should be able to make substantial progress by 6/15. Three runs a week sounds about right for improving without getting injured. Weightlifting on the off-days is a great idea, with whatever program you prefer. Since the new year, I’ve also been biking and swimming on non-running days to get a low impact cardio work-out, but I built my basic conditioning mainly with running. Running’s definitely enough unless you get in the mood for some cross-training, or if you need a temporary substitute because of pain.
At this point, you should have learned that you’ll get a thousand conflicting messages about nutrition. All that crap about PUFAs, SFAs, HFCS, refined food, whatever–I think it’s just noise and distraction. After my seven mile run today, I recharged with 4 chicken salad sandwiches (made with the cheapest supermarket white bread and mayo), and then I ate spaghetti with hamburger and cheese for dinner. I think those were perfectly healthy meals, with lots of body-building protein and other nutrients, but they would probably horrify most of those magazine writers (online or offline). I did have oatmeal for breakfast, but I like it with lots of brown sugar.
Ray Peat’s writings can be fun, but it’s all theory with no empirical backing. The same goes for almost any nutrition theories that get popular online. In my opinion, you’d be better off focusing on your training, and not worrying about diet so much. Just be sure you eat enough (of whatever you like, just as long as there’s some protein and carbs in there), so you can maintain your strength and stamina.