Not a pro here but we have microwave over range and just replaced ours, so here is what I know:

There is no reason a microwave over a range cannot vent outside like a vent hood does. Ours always has. Of course you'll have to have appropriate venting installed if it's not there. When we replaced our 10 yr old microwave, we found one with stronger venting power as well. Something to look for when you shop. But definitely go with outside venting instead of recirculating if you can.

It will not install on a shelf, but on a bracket that mounts on the wall, secured by bolts that go through the cabinet above. I see you don't have a cabinet above so you may need to add something there. A cabinet will not only give you something for the microwave to bolt into, it will also hide the duct work for the venting and prevent you from having open space above the microwave that will just be a dust magnet.

All the mounting equipment (bracket etc) will come with the microwave. I think you will need to supply the venting equipment yourself. I suggest you visit a knowledgeable appliance store (not big box) to get all the info you need, or hire a pro to mount it. When we replaced a broken microwave recently, we chose the same make so didn't need a new bracket, but we still needed new holes for the bolts as their placement had changed. It was a 2 person job for us amateurs to get everything lined up correctly while supporting the weight of the microwave.

The proper height is so that the bottom of the microwave is even with your cabinets, unless you cabinets are mounted at an unusual height. Before we did our kitchen reno 10 yrs ago, our microwave was mounted too high. Not only did it look odd, it was not easy to reach. At the proper height, a microwave over a range is no harder to get into than any of your upper cabinets. People will tell you they think it is awkward or unsafe but unless you are unusually short, I don't think that is the case.

You can look at the same make as your range if you want consistency in handles, although styling changes over time so it may not matter. As long as the finish is the same, it will look fine.

Good luck!

Thank you very much!