OTRs are not flat on the bottom, so they cannot be set on the countertop. Plus you wouldn't want to block airflow to the bottom. However, there is nothing wrong with hanging them from a shorter cabinet just like you would over the stove. I've done several kitchens that used an OTR Advantium hung from a shorter cabinet. They are 15" deep rather than the 12" deep of the cabinetry, so it looks more built in if you can utilize a 15" deep cabinet from which to hang it, but it wouldn't strictly be necessary.

I looked into installing a single wall oven under an induction cooktop (I ended up getting an induction slide-in range though). What was interesting was that most induction brands allowed it IF the wall oven was the same brand as the cooktop. This included Kitchenaid - don't know where you got your information, but the installation instructions do allow for it with certain ovens - it turns out it is the Kitchen Aid single ovens. Two brands did not allow for a single oven under the cooktop even with their own brands (well, it voided the warranty so the same thing): Bosch and Thermador. No problem with Jennair, Kitchenaid, GE, Electrolux, and Frigidaire. I think Whirlpool also didn't allow it, but I wasn't considering that brand. Don't worry about the venting. There is some venting in all ovens - whether built in wall ovens or ranges. The vents aren't any more hot for a wall oven than a regular range. The reason I chose a slide-in induction range had nothing to do with the height of the oven. The wall oven under the cooktop would have been about the same height as a range's oven. Rather, I really liked the Kitchenaid induction with its (albeit small) second baking drawer. I cook a lot and could see using this. Plus, the cost was much less for a slide-in than a separate cooktop and wall oven. Our house is being remodeled and we haven't even been able to move in yet - so I haven't used it. I hope I love it. It does look nice.

A ledger is a board that is secured just below the counter into the studs. It should be 2" deep by 1" high at a minimum. I have a dishwasher that has granite over it with cabinets on either side and my contractor installed a ledger. You will need to have the panels on either side because that is how the dishwasher gets secured. I learned this the hard way. We reused our dishwasher and it was not designed for securing below granite. They put screws into the sides of the cabinets but the dishwasher went out of square and leaked water all over my wood floor. Fortunately most of the water ran into the basement below and my 90 year old floors weren't ruined. We ended up purchasing a new dishwasher designed to be side mounted. But you definitely need something to attach it to.

GE also makes some 24"w microwaves that can be hung underneath a cabinet (the Spacemaker II line), and they've been available for decades, so I wouldn't worry about replacements should Sharp discontinue theirs. Unlike the Sharp, the GE isn't exclusively designed for being hung from a cabinet - it can also be built into a trim kit or sit freestanding on a countertop, so the buttons aren't conveniently spread across the bottom and the bottom isn't as smooth, and there are no lights on the bottom to illuminate your countertop, but it works fine. If you know it will be hung from a cabinet, the Sharp is a better choice IMO. I've used an OTR Advantium without a cooktop below. They show up on Craigslist frequently, typically much cheaper than new ones. There are basically three types out there: a) 120 volt, 15 amp b) 240 volt, 30 amp, old design c) 240 volt, 30 amp, new design All function as a microwave. All can be used as a high-speed oven that combines halogen lamps, sometimes a ceramic heater, and microwaves. Only the 120v model and the new-design 240v (don't remember when the switchover was, about 8 years ago) can be used as a regular oven though (actually a convection oven, but it works the same basic way, by setting the temperature and using conventional heating elements to cook). If a 240v Advantium doesn't have a means of setting a temperature by degrees with the knob, it's the old design. The old model also was smaller inside than the others, didn't have a (removable) shelf inside IIRC, and didn't light up inside unless you pressed a button. If you plan to use the speedcook function frequently, the 240v models work MUCH better than the 120v ones do. That's because they run on twice the amperage as well as twice the voltage, and thus have 4x as much power available to it (7200w rather than 1800w). The microwave draws nearly 1000 watts by itself, so the 120v Advantium has only 500 watts max left for the halogen lamps. The 240v, though, has several thousand watts available for the halogen elements. GE makes clear that the 240 speedcooks twice as fast as the 120; what they don't make as clear is that the 120 relies much more heavily on the microwaves to attain even those speeds, and thus your food won't quite be devoid of that soggy-microwaved texture. I've used both, and the 120 speedcooker is still preferable to a standard convection/microwave and a very nice, versatile appliance, but if you want fast cooking that may fool you into thinking it was cooked in a conventional oven for 40 minutes rather than in a speedcooker for 5, you'll want the 240, even if you have to hire an electrician to run a new circuit. The convection-oven cooking is the same on either the 120v or new-design 240v Advantiums. The microwave is slightly more powerful on the 240 but not by much. If you're thinking of using a portable induction burner below, might as well take advantage of the external venting. Otherwise, I wouldn't bother. Contrary to what someone upthread wrote, wall-cabinet mounted Advantiums with the drop-down doors (except some old ones) are several inches deeper inside than the over-the-cooktop Advantiums, since they fit into a 24" deep cabinet rather than between 12" deep wall cabinets.