You need to warm up properly before you attempt to do any kind of race or speed work. Try run a mile around the track at a very slow pace, then some dynamic stretches then strides.
As for eating - so long as you have fully digested anything you have eaten then you should be ok. No special food to get you to your target pace or we'd all be eating it non stop. Try caffeine, it helps you cope with the pain.
Why not post on the training forum. There are more people there better able to help you. Often people don't read the threads in general. It gets a bit repetitive.
You certainly need to be doing more running. If you can build up to about 25 miles a week with at least two decent track or interval sessions. The young athletes at my ex club ran 3 speed sessions a week but these are kids.
A normal track session I would hope to cover approx 4-6k effort plus warm up cool down and recovery.
Yesterday I ran 2 miles warm up; 10x100m; 6x1,000m with 120secs recovery (should have been 90 secs) 10x100m; 2 miles cool down.
Your k reps should be about 3:25
You can do any reps you like: eg:
2 x800 3 x 6003x 4003 x 200
As I say, your best bet is over on the training forum.