Are 12v power splitter cables device-agnostic?
Yes, such power splitter are just connectors and wires. There's no sort of "intelligence" in these. And as long as the devices get the voltage and can draw the current they need, this should work fine.

1) Yes, should not be an issue, do check that the polarity is correct or you could damage the devices you're connecting.

2) Yes, should not be a problem. Note that the cable where that total 4 A is running needs to be reasonably thick. A proper 4 A or 5 A power adapter will have such a cable.

3) Total maximum power is 12 V, 4 A so that is 48 Watt. Some power is lost in the adapter so total power consumption can be around 60 W that would be around 0.5 A at 120 V AC. On the adapter a higher current might be indicated, this is the peak current it can draw.

The current at the 120 V side will be lower than on the 12 V side. A power adapter contains a circuit which can convert high voltage/low current into low voltage/high current efficiently. If that was not the case your adapter would get extremely hot due to power dissipation.