The first thing to do is to determine what version of the NEC you are under (2005 or 2008), and whether there are any local amendments. You could just wire to the 2008 NEC, but the 2005 NEC provides a bit more flexibility in certain areas.
As fixed in place equipment, it is not required to be dedicated, but it is often a good idea. If the nameplate current draws are low enough, you could combine it with another piece of equipment, e.g. the garbage disposal.
Required to be on a dedicated circuit if cord and plug connected. Otherwise, like the dishwasher.
You could put this on the kitchen circuits (the small appliance branch circuits, SABC); otherwise, like the dishwasher.
There's nothing wrong with putting a fridge on a gfci. If the fridge trips the gfci (as an old one may), then it is leaking current to ground, and should be replaced.
Under the 2005 NEC, you have the option of using a simplex receptacle and a dedicated circuit to avoid the GFCI requirement. Under the 2008, GFCI is mandatory for an unfinished basement.
Since you list a laundry room below, this does not require a dedicated circuit; if it is in the laundry room, plug it into the laundry circuit.
The NEC just requires 2 SABCs, with no limitations on the number of outlets on each. Is this a local requirement?
Likely requires a dedicated circuit, although I'm not sure.
Like the dishwasher, as far as I know.
The dining room has to be on a SABC. So you could combine it with one or more of the kitchen circuits. More common is to run a separate SABC just for the dining room.
How you divide up the remainder of the house is up to you, the NEC does not have a 1 circuit per X square feet requirement. Is there a local code?
Space in the panel for a surge protector?
Lighting circuits and smoke alarms? Whether to wire those separately to mix them with general use receptacles is a personal preference.
Any other fixed in place equipment?
If you modify a circuit, then you have to put in an AFCI breaker if required. Under the 2005 NEC, it is just circuit with outlets in bedrooms ("outlet" includes receptacles and any other boxes, like smoke detectors). Under the 2008 NEC, the requirement is much broader and you should check the details.