Can a range hood go on the kitchen small appliance circuit?

No. NEC 210.52(B)(2) states the small appliance branch circuits shall have no other outlets, with narrow exceptions for a clock receptacle and gas range ignition.

Does a wall oven need a dedicated circuit?

Yes in practice. NEC 422.10(A) requires the branch circuit rating to be not less than the marked rating of the appliance, and a typical wall oven consumes the whole circuit.

Can a range hood be plugged in instead of hardwired?

Yes, under NEC 422.16(B)(4), with an 18 to 36 inch cord, an accessible receptacle, and an individual branch circuit supplying that receptacle.

Can you connect a range hood and an oven on the same circuit?

Almost never, and the reason is arithmetic rather than a prohibition. A wall oven or cooktop is a 240 volt appliance sized to its nameplate under 422.10(A), while a residential range hood is a 120 volt load. Putting them on the same two pole breaker gives the hood no neutral reference unless you run a multiwire circuit, and even then the oven usually consumes the entire circuit rating.

Sizing the oven circuit

Section 422.10(A) requires the branch circuit rating for an individual appliance to be not less than the marked rating of the appliance. For a household cooking appliance, 220.55 and Table 220.55 give you the demand factors for a load calculation, but the branch circuit itself follows 210.19(A)(3), which requires the conductors to have an ampacity not less than the maximum load to be served and not less than the rating of the branch circuit.

A common 4.8 kW wall oven at 240 volts draws 20 amperes, which lands on a 25 or 30 ampere circuit with 10 AWG copper. A 7.2 kW oven draws 30 amperes and needs a 40 ampere circuit with 8 AWG copper. There is no headroom left in either one for a 120 volt hood.

Where the hood is allowed to land

Section 210.52(B)(2) is the rule people miss. The two or more 20 ampere small appliance branch circuits required by 210.11(C)(1) shall have no other outlets, which means the range hood cannot share them. The exceptions in 210.52(B)(2) permit only a receptacle for an electric clock, a receptacle for gas range or oven ignition, and receptacles installed to serve the countertop.

So the hood goes on its own 15 or 20 ampere circuit, or it shares a general lighting circuit that is not one of the small appliance circuits. Most residential hoods draw between 1 and 4 amperes, so sharing with the kitchen ceiling lights is common and code compliant. A commercial style hood with heat lamps and a 600 CFM blower can hit 12 amperes and deserves a dedicated 20 ampere circuit.

If you do combine loads

Section 210.23(B) is the governing limit when a circuit supplies both fixed equipment and lighting or receptacles. Utilization equipment fastened in place, other than luminaires, cannot exceed 50 percent of the branch circuit rating. On a 20 ampere circuit that is 10 amperes total for the hood and anything else bolted down.

Also check the cord and plug question. Section 422.16(B)(4) permits a range hood to be cord and plug connected if the cord is 450 mm to 1.2 m, or 18 to 36 inches, long, the receptacle is accessible, and the receptacle is supplied by an individual branch circuit. That last phrase matters: the plug in option requires a dedicated circuit for the hood.

Field takeaway

Give the oven its own circuit sized to the nameplate. Give the hood its own 15 or 20 ampere circuit, especially if you intend to cord and plug connect it, since 422.16(B)(4) requires an individual branch circuit for that method. Never tap either one off the countertop small appliance circuits.