Hi Sammiez - don't worry, I'm still here and you haven't frightened us off! 
In fact, I really wanted to come back yesterday but we were really busy all day and then my OH was hogging the computer all evening!
I did think a lot yesterday about what you said, and it would be dishonest to say that it didn't upset me. But there is no danger of you "draining the life out of me" and I am genuinely glad that you have felt able to post what you did. However, I am left wondering how to respond, as there is so much that I would like to say to you, that I don't know if I can organise my thoughts properly.
First of all, I am so, so sorry to hear that your dd has been subject to such horrible bullying and prejudice in school. My dd is mixed race (her father is Asian) and it would truly break my heart if she had to endure such stupid, thoughtless behaviour from the other children. I guess we have been fortunate as she goes to a very diverse school where differences are genuinely valued. I'm sure it helps that most of the parents are very well educated - at least half are academics at the nearby university. So we have not had to deal with any of that dreadful rubbish.
However, I know that racism is alive and kicking in some areas - before we moved last year, we lived in a relatively deprived area and the level of ignorance that we witnessed there shocked me to the core. My OH had to endure racist abuse on a number of occasions, and we heard about physical attacks on foreign residents too. This was a huge shock to me, and added to the difficulties that my OH had in settling in to this country. Even though I believe that a small minority of people are responsible for such abuse, it is very difficult to put such incidents behind you.
I really feel that you need to talk to the school again about how they are helping your dd to fit in and make friends. Bullying and exclusion should not be tolerated on any grounds, racist or otherwise, and I think the school has a responsibility to deal with this. Could they assign two or three of the children to "buddy" your daughter to ensure that she isn't left out? It's outrageous that the other kids make fun of her lunch and somebody needs to stop this from happening. I think you need to be quite firm with the school about your expectations with regard to this - and perhaps consider moving her to a different school if things do not improve?
You talked about how happy you were when you first came to the UK, feeling that you were giving your children a better chance in life, and the disappointment that you feel in the way that it has all turned out is palpable. That must be very difficult to deal with. My OH is from a country that was an ex-British colony, and I think he always harboured a secret respect for the country that had somehow managed to rule half of the world. I guess he assumed that our civilisation must somehow be more advanced, more developed - not only economically but in all aspects. After coming to live here, I think he felt a huge disappointment in the realisation that actually, the UK is not so advanced at all - not in the areas that count. In some ways, he perceives our society to be quite backwards - our families are falling apart, we have lost the sense of community that once held us together, and we have become very materialistic. And the level of education among the general population is not high. Perhaps it sounds strange, but I think he found himself feeling quite bitter about all this - as if he had somehow been deceived. I don't know if that makes any sense.
I totally agree with ZZZenAgain that you sound infinitely "better educated" than many native English speakers. And as for struggling to understand their language, even I had difficulty understanding some colloquial speech after living overseas for a long time - lots of people just don't enunciate their words properly! Yes, there will be little bits and pieces of knowledge that your dd picks up from school which will be unfamiliar to you, but that is the same for all of us! And really, it doesn't much matter if you know what a wombat is or not! I'm not sure if I know myself what they are supposed to look like!
From all that you have said, it sounds like parenting in your home country is very different from how it is here, and I'm sure that there are things that you can learn from how we do things here. Having said that, there are probably just as many things that we could learn from how you do things over there - you only have to look around you to see that we haven't got things quite right over here either. One of the things that I have greatly enjoyed about being married to someone from a different culture is how we can pick and choose the best bits of each - I really don't think anyone has all of the answers! For example, we co-slept with our dd from when she was a baby until quite recently, and the health visitors and most of my British friends thought we were crazy. However, it's just what people do in my OH's country and it felt right to me at the time. My dd is one of the most secure and confident children I know, and I still believe that that's in part due to the co-sleeping.
I feel that I'm rambling now, and perhaps not making much sense. 
I so wish that there was something I could say that would help you to get through all the difficult things that you are going through, sammiez. I wish, too, that we were a bit nearer to you so that I could offer some kind of practical help, but we are nowhere near Hertfordshire. :(
I can understand how difficult it must be when you don't feel that you have the resources within to offer your daughter the comfort and reassurance that she needs, but you mustn't blame yourself for this - depression can be debilitating. I still think you need to prioritise your own wellbeing somehow, and find some kind of support network - it's a bit like being on a plane, you have to put your own oxygen mask on first before helping your children. This is easily said and not so easily done - I need to think more about how you might be able to get some support. Have you tried contacting the organisation Homestart? It might be a good place to start.
If you are willing to say which part of Herts you are in (even roughly), then perhaps we can find some other ideas that might help. But again, I understand if you would rather not give out too many details on here.
There is still so much more that I want to say, but I can't easily put it into words. I have to go out soon, but I am still thinking and will come back later if I can.