Could you please ID this plant and advise how to care for it. Supposed to be...
Yes, this does look like a cherry. Although we can't say for sure from the photo, the leaves do look alternate (they alternate on the branch, as opposed to being in pairs opposite each other). There are many species of cherries, and this looks like a sweet cherry. The petiole on a sweet cherry should be 1 to 1 3/4th " long (the petiole is the little stem at the end of the leaf that attaches it to the woody branch.) We can't see any petioles on the photo, but you can check that out if you like.
If you want to grow this tree for fruit, you'll want to prune it in late winter (around early March) just before it leafs out.