For systems involving sumps, you have a lot of choices. You can use an insump pump such as a Mag and they will work fine.
However, I usually prefer externally mounted pumps, such as Iwaki. They will be more expensive, but will last almost forever. You'll have little trouble going up 7 feet, and across 4 with an external pump. External pumps can make more noise though, and it's much more involved to plumb one correctly.
You won't get much flow with that much lift head on the Eheim. You can do a quick test by just putting it in place in a container of water and attaching some line to it at the proper height and watch the output as you raise and lower the line.