volunteers

I have found two more little evergreen trees of some kind growing in the grass. They're very small, and have a different look from the ones in the front I moved into the flower bed. I'm thinking of digging them up and putting in pots to watch grow bigger and see if I can identify.

Against the side fence in the back near shed two little shrubs are sprouting from the scraggly grass, too. They seem to be the same as the scrawny shrub against the fence that has small, dark blue berries in winter (I don't see any birds visiting it). I want to try and figure out what these are, too. Is it something planted on purpose? a native? an invader? worth growing and can I prune it to make it look nicer and full?

Here's a bit of twig I pulled off to look at closer. I pored through some tree-and-shrub identification books at the library today, but couldn't decide what they were.