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I couldn't find a direct up-to-date answer. For example the comments on this answer contradict each other.
So, which of the following kitchen appliances are allowed to be grouped onto the same 20A circuit (USA)?
For the five kitchen appliances (and one lighting system) described in your post, the answer boils down entirely to wattage/amperage draw, as there are no specific requirements in the NEC for any of them to be on dedicated circuits; the fridge could be on a small appliance (kitchen countertop receptacle) branch circuit, and the remaining appliances can be on individual circuits or combined together as wattage permits; likewise, while the undercabinet lights can't be on a kitchen countertop circuit, they can go on any general lighting and appliance branch circuit that has the wattage to spare.
However, there are some constraints. Dishwashers, disposals, and microwaves all tend to be power-hungry beasts, meaning that you're going to have a hard time fitting even two of the three on the same branch circuit, and putting all three together on a single circuit is a non-starter. The fridge is the other constraint; if it's not on a kitchen countertop branch circuit, it must be on its own circuit, not a general lighting circuit. Given all this, I would look at pairing the dishwasher and disposal, if feasible, and also at putting the range hood and the undercabinet lights on the same circuit, given that you don't need a colossal commercial-style range hood to deal with domestic cooking needs, even if you have a jumbo range. (Commercial hoods are as beastly as they are because they have to keep air pollutants within OSHA limits throughout a restaurant cook's eight-hour shift despite near-continuous use of the appliance beneath them.) The microwave and fridge then wind up on their own circuits.
As to wiring methods, while there's nothing in Code that depends on that factor, the judicious use of individual THHN wires in ENT conduit ("smurf tube") can provide a major upgradeability benefit down the road. This is particularly handy in hard-to-upgrade spots, like when feeding the dishwasher and disposal, or for kitchen islands for that matter. You'll also have to make sure that you don't violate the 80% maximum total load rule for fixed cord-and-plug loads and the 50% maximum total load rule for fixed hardwired loads on convenience circuits (i.e. circuits that serve receptacles and/or lighting).
