Not advised to create a ledge. You physically can, but now you depend on silicon to keep things water tight. If you keep a zero reveal or an overhang, then water is less likely to accumulate on the sink flange (Which is used to create the ledge). The silicone then can stay intact longer, and not be needed as the primary water guard. Often the biggest problem we see with ledge sinks is with the installation. Some issues we have been told is with accessories not fitting. However, this is easily avoidable with two best practices: 1. The fabricator should always follow the template 2. Once the hole is cut for the sink, dry fit the accessories to ensure smooth sailing from the client. If you like ledge sinks then check this new release: Kraus Kore

Could you unfasten the sink cabinet and pull it forward a few inches so that it's deep enough to accommodate a standard sink? It would require reworking the cabinet, matching the existing finish and having an offset in the counter top. There's another problem; the 30 inch width probably means a double bowl sink won't fit. Beyond that, it doesn't sound like a dishwasher will fit in these shallow cabinets. If I were you, I'd replace the lower cabinets!

I won't recommend specific hoods that I haven't owned. Performance requirements first, cost vs. aesthetics to meet performance second. Assuming a wall hood... Overlap is needed front-to-back as well as side-to-side. Assume a hood entry aperture of 42 inches by 24 inches (from a 27 inch deep hood). This is a hood entry aperture area of 7 square feet. You will need 90 CFM/sq.ft. for containment of hot gas combustion products and hot oil from stir-fry. So the requirement is to be able (on high) to pull 7 x 90 = 630 CFM. To do this with typical pressure losses in baffles and ducts, a 900 CFM rated blower will likely be required, consistent with your plan. However, this assumes that the house interior pressure is not reduced (relative to outside) by more than a few hundredths of an inch of water column. Most code authorities now-a-days will be enforcing make-up air (MUA) above 400 CFM (rated). You will need either a large duct opening outside with damper and minimal filtering (perhaps dumping air into a mud-room or basement with a powerful enough heater, or a powered MUA system with filtering and heating, depending on environment. The latter alone will eat your budget. For the hood itself, one is best served by a commercial-hood-inspired configuration (often called "Pro") with a capture volume before the filtering and baffles for filtering. Ducting out the wall or up through an attic are both appropriate, but using a remote blower and intermediate silencer will yield a lower noise configuration if enough duct length is available. No matter which duct layout is chosen, capture volume and baffle filtering will preclude a thin under-cabinet hood. Bottom line, a kitchen ventilation system suitable for the specified range may not cost as much as the range, but will not be far behind if the residence is to be kept free of greasy wet cooking effluent and the hazards of dropping your house pressure are to be avoided.

Does it has to be 36"? The GE JGS760SELSS 5.6 cu. ft. Slide-In Gas Range with Self-Cleaning Convection Oven in Stainless Steel looks "classy", is recommended by Consumer Reports, is liked by Home Depot owners, and costs $1300. More upscale (but not better performing)? GE Profile PGS930SELSS 5.6 cu. ft. Slide-In Smart Gas Range with Self-Cleaning Convection in Stainless Steel ($2100).