Hi and welcome. I'm no expert but have blundered through 2 HMs and am not a natural runner, so maybe I can help.
With distance, make sure you are having rest days. If I run more than 50% of the maximum distance I can run, or I do an intense speed session, next day has no running for me. Those rests are essential.
To increase distances you're running, I think you need to bring your speed right down. I find it hard to run really slow, but you have to force yourself. Aim to run maybe 800 metres more than last time - you should add no more than 10% each time. I ask myself what the purpose of each run is. Is it intervals (short distances, top speeds)? Is it distance - no pressure on speed, just a long plod?
Not sure on the eating, but make sure you get some protein and carbs after running. My easy way s cook cous cous and throw in lentils and other beans.
Shouders came up on the Runners sub forum a while back, take a look. Basically you need to flex them and extend your range of movement while you run.
Hope that helps, let us know how you get on.
You can see my training log if you're really bored: [url]www.veganfitness.net/viewtopic.php?f=8&t=16086&start=360[/url]