Well, it is a little hard to plug two appliances into the same outlet unless it is a multiple receptacle outlet. ;D

Outlet. A point on the wiring system at which current is taken to supply utilization equipment.

Receptacle. A receptacle is a contact device installed at the outlet for the connection of an attachment plug. A single receptacle is a single contact device with no other contact device on the same yoke. A multiple receptacle is two or more contact devices on the same yoke.

Receptacle Outlet. An outlet where one or more receptacles are installed.

Branch Circuit, General-Purpose. A branch circuit that supplies two or more receptacles or outlets for lighting and appliances.

Branch Circuit, Individual. A branch circuit that supplies only one utilization equipment.

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If you wanted to know if it should have an individual branch circuit, then that depends on how many amps the freezer draws, and what other things might be plugged in on the same circuit. If it is just a clock, then no problem. If you want to plug in an air compressor or table saw on the same circuit as the freezer, then you may have a problem.

It is hard to tell where someone may eventually put a freezer in a garage on new construction, so it can be a bit futile. If the freezer has a dedicated space inside the house, it may be worth dedicating a circuit....

If the freezer has a 15A plug (two parallel blades possibly with a ground pin) then it's not drawing more than 15A (likely not more than 12). As pointed out, whether or not a GFCI is required depends on where the receptacle is located. If it's in a garage, for example, it requires one. If it is in a kitchen, provided it's not serving a countertop or closer than 6' to the sink, it doesn't.

For practical matters, you may wish to have a dedicated circuit to avoid having other devices on it that may trip it. On the other hand, unless the freezer is in a place you pass frequently and has a pilot light or something that lets you know it is running, you may wish to add something to that circuit to let you know if it was tripped before the food in the freezer starts to melt.

I looked for years for a reasonable freezer alarm with no luck. I finally saw this one not too long ago. It is reasonably priced and works well. The required lithium batteries for the sensors are costly, but there is really no way around that.

I have not checked since I bought this model so there may be something better at this point. WiFi-connnected would be nice and may well exist at a low enough cost by now.

AcuRite refrigerator/freezer thermometer.

I was under the impression that devices which never should be turned off (refrigerators, freezers, smoke detectors, etc.) should not be put on GFCI-protect circuits.

There used to be an exception in the NEC allowing a dedicated single receptacle in places that would normally require GFCI protection (like a garage) to be unprotected for a freezes/fridge, but they took out the exception.

There are still plenty of new fridge/freezers out there with a motor leakage current that will trip a GFCI even though the UL standards for refrigerators has changed to meet the GFCI leakage limit.

So, Fred, what prevents an unobserved GFCI trip, which will cause all your food to spoil?

Nothing.

Yep, you either put something else on the circuit you'd notice, get a freezer alarm, or you put your freezer some place where a GFCI is not required. I suspect the problem with garages and the like is that people have been known to unplug the freezer (either temporarily or just to remove it entirely) to plug in something that ought to have such protection.