Hi and congratulations on becoming a human slave to 2 Lovebirds! They are small parrots with huge personalities and, once they become comfortable with their new surroundings, have a knack for getting into anything and everything!
First I'm going to address Mali. Based on your description of how they interact with each other, my guess is that you have 2 females. They beak spar or get into squabbles and that's typical of females. Two males are usually happy campers together and a male/female pair usually get along very well together once they get to know each other. Will that be likely to change? Nope. They will always have to have their own cages and be supervised when out of their cages at the same time. Make no mistake about it. Those squabbles can turn deadly and the dominant bird, Blue, could easily kill Mali.
You say you got Mali from a pet shop and she may have been friendly at one point, but most pet shops don't pay enough attention to their birds, particularly lovebirds, so they revert back to being wild. Mali will eventually learn to trust you (by experience) and you will see that her interactions with you will change but that simply takes time and more interaction. I would remove the toy with the mirror. Lovebirds form strong bonds with whoever/whatever they like and it's very easy for them to bond to a reflection in a mirror that is not real. As for not playing with toys, Mali simply doesn't know how to play. With my lovebirds, favorite toys are swings and bells. When getting bells, this is the kind I use for all of mine:
https://www.amazon.com/Stainless-Han...8155640&sr=8-9 For lovebirds, I would get a small size one so that it's not overwhelming. The clapper on this particular bell is up inside the tube and cannot be removed and swallowed. I toys that I buy have other kinds of bells attached, I remove them or just remove the clapper.
Lovebirds are native to Africa and they have a higher dietary fat requirement to remain healthy. This is true of all African species. I have several African Greys and they need their sunflower seed. Pellets are typically low fat so I don't use many. Some seed mixes contain a few pellets and that's OK but my own avian vet does not recommend an all pelleted diet for Lovebirds. Her recommendation is no more than 20%. I use even less and I have several Lovebirds who are in their late teens, age-wise.
I would love to see pictures of Mali and Blue. I may be able to tell you more about them if you choose to share. To post pictures here, upload them to an online storage site such as Imgur and copy/paste the image URL here.
Hope this is helpful.