I would like to know the names of these trees. And whether the small black berry looking fruits are edible.
Edit: The small tree is not doing well, so I want to learn more about this tree in order to give it the best chance to survive.
Gardening & Landscaping Stack Exchange is a question and answer site for gardeners and landscapers. It only takes a minute to sign up.Sign up to join this community
The first one looks like Hawthorn, or Crataegus. But for more specific ID we need to see the fruits as well. See here for an example with the same leaf shape.
The second one is a Prunus, I think a Prunus serrulata 'Royal Burgundy' (as seen here), but it could be another variety as well. This cherry tree is more ornamental, and not meant for fruit production. So the fruits are edible, but won't taste as good as the real cherry. See here about edibility of fruit that come from ornamental trees.
Your trees look indeed not in perfect shape, and stormy gives you already some advice. Maybe more people (arborists) here can give you more advice.