The fighting might be a territorial thing. I've heard people have success with placing both the mice in a plastic tall tub with nothing in it including bedding...just until you de-scent the cage and remove all toys or anything that can be fought over. I find that when I need to switch around cage mates I need to soak everything possible in bleach water and clean the cage out with bleach...including the food dish and water bottle. Once everything is washed and dried put just the water bottle back in with bedding and nothing else then put the two mice in together, put food on the bedding and not in a bowl. Leave them like this for a week and if everything settles down and they get along then I put dish and toys back.
As far as being shy, I have success with just putting the mouse in a small tall plastic tub that can't be jumped out of and going to sit somewhere like in front of the tv. I then place my hand in the tub and just rest it there. I let the mouse come check me out and eventually they crawl in my hand and up my sleeve trying to get out...lol. I don't ever chase the mice to scoop them or anything that would make the mouse feel threatened. When I need to take them out and they don't want to get in my hand then I use a toilet paper tube and let them run into it to lift them out.
I do have a few that are hyper like your mouse...and they can be tamed but they usually stay hyper, they just get in my hand really fast now...lol!
As far as being shy, I have success with just putting the mouse in a small tall plastic tub that can't be jumped out of and going to sit somewhere like in front of the tv. I then place my hand in the tub and just rest it there. I let the mouse come check me out and eventually they crawl in my hand and up my sleeve trying to get out...lol. I don't ever chase the mice to scoop them or anything that would make the mouse feel threatened. When I need to take them out and they don't want to get in my hand then I use a toilet paper tube and let them run into it to lift them out.
I do have a few that are hyper like your mouse...and they can be tamed but they usually stay hyper, they just get in my hand really fast now...lol!