Paint, yes I've got experience of weaning at that age, back in the olden days
. Its a lot of faff, DD will take ages to eat a small amount and probably won't be getting any more calories as, before 6 months you can only really offer fruit and veg. There are far more calories in BM and having weaned 2, one at 16 weeks and one at 23 weeks I really, really would recommend waiting.
As for the hungry baby milk, did you know that it does not contain any more calories then regular formula? It just takes longer to digest. If you baby is hungry, then feeding less often means less calories, not more.
When you say she is hungry, how often are you feeding in the day? Is she feeding more often than every 2 hours? Have you tried breast compressions? Are you getting enough wet nappies and is she bright an alert at times?
Hungry babies are often lathergic and from what you've said she sounds like she is meeting all of her milestones and watching what you do, eating, cooking, putting on your makeup, is all normal baby behaviour.
As for waking at night, it could quite easily be the the 4 month sleep regression. It could also be the 4 month growth spurt or any number of other reasons. Babies do wake and it is normal. By 12 months half of all babies still wake, no matter how you feed them or parent.
Also, by offering formula and/or solids you might actually get less sleep. DDs digestive system isn't mature enough to handle solids really and she may wake with indigestion. Certainly my experience of weaning at 16 weeks was that my baby was more hungry and woke more often, sometimes screaming with tummy ache. Have a read of Will offering solids or formula help my baby sleep?.
Personally, I would stop offering the bits of food to play with too. 6 months is only a guideline but I would be worried about choking at that age. If you do want to perserve with the weaning I'd recommend going on a Paed First Aid Course. Could you just give her an empty bowl and spoon to play with instead though?
MN has got some good information on weaning here, the NHS stuff is here and you may also find this interesting reading.