£800 is not an excessive amount to spend on carpets for an entire house, and means it is warm, welcoming, clean and feels like your own home having got rid of the smell of previous owners' dogs, cats, cigarettes, takeaways, bicycle oil or whatever else they were in to .
hose little cooker thingies are fine - we used one for months when we first got married, then DS took it when he moved out (25 years later). When he got a "proper" cooker, he gave it to a friend of his and as far as I am aware it is still going strong. (After nearly 40 years). We even had a teeny-tiny yorkshire pudding tray to squeeze into it.
There are only two of you - that chances of you needing to cook a 58 lb turkey are pretty remote.
Your ex is being a tosser - as others have suggested, tell him that if he is really worried about your daughter's nutrition, you would be delighted to accept and brand new shiny proper-sized oven from him on her behalf. Othrise he can go and do one.
The odds are he feeds her chips and Gregg's pasties when she's with him anyhow.
The wanker. 
(How are you managing for furniture BTW? It's just that there may be other MNers local who have stuff they are replacing but which is decent, and they may be able to help. Best of luck to you and your daughter anyway. Your are better off without such a snide man in your lives.)
Have some 