I'm having trouble picturing your layout. Is the stove going directly beneath the window? Is the window right at the corner? If the stove going in directly beneath the window, if so, is the back going against the exterior wall with the window or against the interior wall that is 90 degrees to the wall with the window? Is the stove going exactly in the corner or do you have countertop that makes an "L" with the stove just beyond the L? Are the ceilings 8 feet high? Maybe you have a galley style kitchen with the counters running perpendicular to a wall with a a doorway aat one end and a window next to it? I ask all this because my first thought was to ask why get a ductless hood (a "ventless vent" as it were) if you've got an exterior wall? Almost all wall-hung and cabinet-hung hoods can vent directly out the back through a wall. If the stove backs-up against an interior wall, it is easy to put an elbow on top of the vent hood and take it out the side wall -- unless, of course, that is where your window is. Do you condo association rules prohibit exterior venting hoods? As for"is it possible to mount "under cabinet" hoods NOT under a cabinet?" --- sure. Some under-cabinet hoods are constructed so to give an option of wall-mount or hanging undercabinet, but it will be easier (and more stable with less vibration) to hang most such hoods from a couple of upside down shelf-brackets -- or make a shelf and hang the hood from that. Putting a ventless hood 44" above the countertop strikes me as likely to be ineffective for grease. It is so far away from the stove and the fan power in most recirculating hoods is so low that it cannot capture much grease or steam. Most of the effluent will begoing to go on the walls, the window and out into the kitchen. Frankly, I think you would have more luck just putting a box fan in that window whenever you wanted to vent. Also, consider how high you'd have to reach to hit the switches on a recirculating hood that is placed that high. Think about reaching to the middle of the lintels over the doorways. Maybe not so big a deal if you are tall, but likely an annoyance nonetheless.

No, unfortunately there is nothing even remotely comparable to the Ventahood.

I think ARS might be better than other recirculating though I don't know that for sure. Good ventilation (HRV/ERV) will help but it could take 24-60 hours to remove contaminants. And that's assuming good ventilation which something like 97% of homes in the U.S. do not have. Contaminants really need to be removed at the source. Once they spread in to the house it will take a lot to get rid of them. These are gases and particulate matter that you are not necessarily going to notice in any way. But they slowly degrade people's physical and cognitive health. People can say that they've had a ductless for years and thought it worked great but I've not yet seen any of them provide measurements of VOC's nor medical test results from before and after. We measure O2, O3, CO, CO2, NO2, and CH2O along with PM1.0, PM2.5 and PM10 on a continual basis and the results can be quite scary. Some of what's coming out of EU and LBNL recently is quite eye opening. Given what we now know about indoor air quality and health it's irresponsible to not install a proper range exhaust system.

”Ductless” is a misnomer. Recirculating is the correct term. That means you have to provide a route in and out both for the air to be able to come out somewhere. You need a custom stainless insert for the bottom, to cover any of the exposed wood, or you’re creating a fire hazard. Plus you need a big ugly opening grate for the air to recirculate. Or to duct it into an adjacent room, etc etc. Lots go into this, to make it safe and effective. Otherwise it’s a grease catcher that has a high risk of catching on fire.