Training tips for running challenge?

Looks like you are burning off an extra 1500-2000 calories per week which is not a great deal or a little more than half a pound of fat. You should be eating plenty of pasta as well as fruit and juices to replace the minerals you loose in your sweat. There is no need to starve yourself if you are running 5/6 days per week.

I'm a running strict vegetarian. 1200 calories is way too low. You pretty much should double that.

You should be able to run an hour a day 5 days a week, and maybe 2 (slowly) once a week (without any issues or weight change). Is that enough to keep you in first place?

Every night before you go to bed blend up a quart of smoothies. split them up into 2 - 4 shaker bottles - you can freeze some. Eat your regular meals but drink a smoothie between each meal.

use soy milk, peanut butter and bananas, you can add soy protein powder if you wish. If you get tired of those there are plenty more recipes. But I especially like that one cause its good with calcium, fiber, protein, and potassium - all the things a runner needs.

Big increases in activity level should be taken gradually, so going from 5km a day to 10km a day might take a month or so, in that time also have a few gym days and then a rest or easy day. You might find that your increased distance will make you faster - which could be a good thing

Nutrition. Yes, you might need to eat more (generally women are advisd to eat 2000 calories a day). I don't know what you eat or how you eat but one tip might be to eat smaller amounts but more frequently, so smaller breakfast, lunch and dinner but add or increase the size of a morning and afternoon snack and supper. Maybe adding in cereal bars, nuts, and so on. Also one tip might be to add more cheese to things (more energy in that and calcium). You want to maybe go up to 1800 calories when you run 10km

As for continuing to eat healthily - you should consider your whole diet and remember than the odd 'bad' food with your general diet can be OK, life doesn't have to be all about beans and pulses....

Ah yes vegetarians and calories. I was a vegetarian for 7 years. I got too sick in the end.

If you are not vegan try eating eggs for the protein. If you are vegan try eating more soy beans for the protein. Protein will help build muscle. Muscle weighs more than fat.

If you are interested in this option you should be able to get some vegetarian protein powder. You can make a smoothie with soy milk, protein powder, perhaps add a banana, honey if you want, or anything else that you may like. You could have a couple of these a day as a snack. If you drink cows milk then use that if you prefer. Some of these powders are used by body builders to weight gain. You can often get them in a supermarket.

Eat more nuts, pumpkin seeds, muesli bars. As a snack try a bowl of rice and raisins (hot or cold). Use something other than raisins if you don't like them. Another snack could be porridge with something added like banana. Crackers with avocado and any other salad vegetables.

So if you eat breakfast, lunch, and dinner, try adding a snack mid morning and mid afternoon.

If you already eat mid morning and mid afternoon, try adding a snack between breakfast and mid morning, and between lunch and mid afternoon.