Some people seem think that if you clip a finch's wings and work with it that it will become tame like parakeets do. Who knows, maybe they would. I would not want to risk it. Finches can not climb around the cage like hookbills do and without their ability to fly they would not be able to reach the perches, food, or water. In short, it would probably die before taming.
Finches are pretty birds.
You look at them, they sing, they beep, and when you have a male and female together, you will get more of them. I have a had fed finch, she is very friendly, very loving and she has run of the house. There is usually one aggressor, or one pair that acts as the aggressors in a colony or flock. Watch your birds for while to figure out which bird or birds is being the most aggressive and remove them. Once the aggressive birds have been removed there may be a little bit of lingering hospitality among the rest of the flock but that should calm down after a few days.