I agree, she doesn't need food in the night and heartbreaking though it is, giving her milk could then create a hunger for it. Think about it, if you have a snack and a cup of tea at 11am every day, soon at around 10:50am, your stomach starts to rumble because you've been trained to have it.
My LO isn't as old as yours so I've not tried cutting out night feeds with a child of that age but one thing which is often suggested is offering water rather than milk, it might be a gentle way of weaning her off waking.
As for food during the day, what does she like? Although it might look like my LO grazes, he has 3 meals and 2 snacks a day at regular times and I eat with him for two of the meals. I think it's important not just from a calorie intake but also if you're snacking it's not the most balanced meal, it will cause more tooth damage constantly eating little bits but she's also missing out on the social side of meals.
The fact she tries stuff though is really encouraging. Is it feeling full, distraction or some other cause which stops her from eating a full meal? I think that is the thing to work on IMO. Perhaps as she likes to try things you could try for at least one meal a day having a selection of food out, e.g. if you were doing a sunday roast having loads of different vegetables in dishes, giving her the choice might make her eat more. In fact I remember reading some research on this. You know if you have a platter of mixed sandwiches vs. a platter of the same sandwiches (even the ones people like the most) people will eat more if there is choice!
Have you tried involving her in cooking as well? I'm really looking forward to doing this with my son and I hope I will pass on my love of food through it. A simple thing to try is to make pizzas and get her to choose the toppings and put them on. If you're a bit busy (being pregnant an' all) you could get her to choose things in the supermarket instead?