In terms of weight, 1-2lb a week would be a healthy rate of loss. Running is good for weight loss, but sometimes people can get in the mindset that as they are running they can eat more, and the extra food means no weight loss (or gain) so worth keeping an eye on that. 30 mins running will very approximately burn up to about 300 calories.
I would not say that anything is needed after 30 mins of running, though I know nothing about vegetarian diets. I would think (hope?) though that your normal diet would provide what you need to cover what is needed - like I say though, others more knowledgable may say otherwise. However, bearing in mind you will have burnt say 300 calories, I think it will make the weight loss tricky.
In terms of making it a habit, have fixed times to do it - same time of week, or schedule it in your diary each week. Make it easy - have what you need ready and easily accessible. Have a few routes for variety, and so that you don't have to 'think' about possible routes, and that you feel ok running in the dark (e.g. well lit so no problems with tripping etc). Go in the morning if you can (though I find that very hard as not a morning person!) - leaving it to later makes it more likely 'stuff' will happen, and you won't go. In terms of running in the cold - if you dress appropriately once you are out the door it is fine. You don't need a whole heap of expensive gear, bu a few choice things to deal with the weather. Is there anyone in a similar position who you could run with sometimes - bit of healthy competition, and always easier if you are meeting someone for a run. And I think my cardinal advice is, if you run in the evening after work or whatever - just go, do not under ANY circumstances, sit down

.
And tell people what you are doing - more motivation to keep going. Sign up for a race (5k say). Google Park Run - weekly, free 5k which you can race or just run. You'll meet people and it will help with the habit stuff.
3x30 mins a week is fine if that is what you want to do, and getting into a habit is a great start. But if you want to run for more than just weight loss, that could get a bit monotonous. Come back on here then and ask what you could do - loads of things, so don't let boredom be what makes you stop down the line.
At the end of the day only you can do it, but plenty of people do, so you CAN do it!
Good luck.