Your DD sounds a lot like my DD1 was a couple of years ago. She is a very high needs child, needing to reassured a lot, hence asking for more milk and wanting to sleep near me. Yet being independent and well behaved with other people.
In the long term try not to worry, my DD1 outgrew both the excessive milk demands and the nightly co-sleeping and your DD is likely to do the same even if you do nothing. Now at 4 DD1 only has milk maybe once a day in the evening and only co-sleeps once a fortnight.(if that)
My 2 year old DS has just hit this stage a few months ago too. You can either fight it and reap the resulting bad behaviour which may or may not settle or just go with the flow until this phrase finishes on it's own.
With my DS I usually give him breastmilk on request. Though I negotiate, so milk is offered after meals not before and he has to ask nicely with please and thank you and no pulling at me or shouting. You can insist on good nursing manners.
Regarding solids, it doesn't matter if she is fussy at home, if she is eating milk at home and some food for other people...that should be enough for her. I would check with a doctor whether they would recommend any vitamins etc whilst she is being fussy. My DS eats three full meals plus snacks and still takes a lot of breast milk too, even if your child was to start to eat properly, this might not reduce the need/desire for your milk too.
Re sleeping. If she doesn't want to sleep upstairs on her own, why not put her to sleep on the sofa downstairs and take her upstairs when you go to bed. We do this with DS, he is not allowed to play with toys or watch tv and the main lights are dimmed. He will often fall asleep within half an hour of loving enforced boredom.
I find if I let him co-sleep and he has reasonable access to milk, he is relatively well behaved and rarely tantrums. If I try and change these things his temper gets worse and he has more tantrums. This proves to me that he still needs to be close to me at night and needs the reassurance/comfort of nursing. Just like his older sister did at the same age.
It is a no brainer for me, he is much easier to parent when I met his needs, at 2 years old, he is still a baby in many ways.
Good luck.