Did I miss this answer, or can you not use the telescoping downdraft mentioned earlier? I think any of the ceiling options are going to look a little odd; a hood hanging down in the middle of that small space will be the first thing you see coming through the door. So my first choice would be a downdraft (if architecture allows for the venting), and I know it isn't considered ideal but perhaps there is one that will work adequately. My second choice would be to just let the ceiling ductwork be exposed. Surely the industrial look would fit in a rowhouse? Perhaps the ducting could even be painted. I am not sure what's possible... I have seen painted ceiling ductwork in public buildings, though possibly we are talking about different kinds of ducting material.

You cannot duct into a chimney, but you can run ducting through the chimney as a sort of soffit that contains that ducting. Ducting for range hoods needs to be rigid smooth metal so as to avoid grease buildup. Even if you have a terrific range hood with high CFM and an excellent filtration system, the air that passes through it will still contain lots of microscopic grease particles that can attach themselves quite easily to a rough surface like masonry. Then they build up. That's a fire hazard. It's a particularly nasty fire hazard if this is an old fashioned non lined masonry chimney that already has it's own buildup of creosote from being used as a wood fireplace.

If you must turn to strangers on the net because you dis-trust people you hire,you have a much larger problem than water in your ducts.

The assessment of trades above by @User is correct. You’ll need a HVAC person, an electrician, and someone to do drywall. You’ll also need a new dedicated electrical outlet for where you moved your MW. I’m not sure why there isn’t an outlet above the range, where you moved it from, but it wouldn’t be in the right place for a chimney hood if it were. That’s why you have to decide on the hood, and design everything around the exact hood’s specs. The location and shape of the duct and the electrical location is NOT universal. It’s normal to have to move or adjust everything, or do new. You need the specs and the hood on hand when talking to contractors. Don’t forget an exterior damper to keep cold air from infiltrating your home! You will get a better job, done faster, if you hire a General Contractor, rather than trying to hire the trades individually. They have their subs that they give lots of work to, and who will return phone calls and show up. And pull the permits that this will require. A homeowner doesn’t get the same price or response from the trades, and it takes weeks longer. I’d suggest posting on your local NextDoor or Facebook neighborhood or city group to look for a licensed and insured (check this!) contractor who can do a small job. But, it isn’t as small as you think!