First, take any hardwired loads (and I count installed appliances like microwave and dishwasher whose sockets are only accessible by pulling the appliance). Take their amp rating. If they are a water heater or could plausibly run for 3 hours, add 25%. Total up the hard-wired loads for a circuit. If they take more than 50% of available amps, then you can't have any receptacles on the circuit.
This makes many circuits effectively "dedicated", except e.g. a built-in 11A microwave could share a circuit with a 1A exhaust fan, but not receptacles.
Kitchen receptacle circuits are a big mess in Code. In Europe, most heat appliances like grills, kettles, coffee makers etc. are 2000-3000 watts. However, in the U.S., they are clamped to 1500 watts due to our 120V voltage, and every manufacturer uses all of it. Kitchen receptacle circuits are 20A (2400 watts) -- which means if you run two heat appliances at once, you probably trip.
That is why NEC requires two countertop circuits. However realistically that is not enough. Wanting to toast your hamburger buns while the Foreman grill cooks your burgers is perfectly reasonable, and "2 circuits" is no protection - it only means a 50/50 chance of both being plugged into the same circuit. This ends up being a minefield for the chef, because they don't know which receptacles are on which circuits.
Well, hold on. We don't wire electricity to pass code. We wire electricity to use it. So my philosophy is think about how the kitchen will be used; if you do more than reheat Chinese, then I would just "cut to the chase" and fit 1 circuit per receptacle. You can explain that to the chef in 10 words.
The refrigerator has a lot of options, and it is often put on the kitchen receptacle circuit. While legal, it's very undesirable. First, if you get into the "2 heat appliances" bind, you'll trip the fridge too. Second. receptacle circuits must be GFCI. You really, really, really do not want the fridge on GFCI protection; it's grounded, all the sparky things are in the bottom back, and you're unlikely to drop it in your sink. However fridges tend to trip GFCI's quite a lot due to their big electric motor.
All of this tends to add up to "dedicated circuit for fridge".
On the duplex breakers, which I like to call "double-stuff", those are fine, with a few caveats.
- You must never, never even think of hooking one to a multi-wire branch circuit, because it will overload the shared neutral. It must be two completely separate circuits with separate neutrals, wired in dual /2 or single /2/2 cable. Never /3.
- This type of breaker is not available in GFCI or AFCI, so it can't be used on an AFCI circuit, and will require a (cheaper) GFCI deadfront or receptacle if that is called for on that circuit.