Voltage/Amperage load rating
How a device will respond to the wrong voltage will depend much on the type of device. A resistor for instance getting half the voltage will dissipate 1/4 the power, and that's it. For motors like the fan it's different. A slightly lower voltage, like 10 V, will probably not be a problem, but at 6 V it may not start. Same here: it only get 1/4 of the required power, and that may be insufficient to get it going. But it may run if you would hand-start it.

120 V will kill it. Final. It's 100 times the rated power and it will burn, possible burst open with a small explosion and some smoke.  

A slightly higher voltage than rated for won't do too much harm, but I would avoid it, again for the same reason: power is proportional to voltage squared, so 10 % higher voltage will give 20 % higher power, and since much of the load is resistive it will get hotter. 

If your solar panel can supply 160 mA, and you would connect four 160 mA loads in parallel to it it would get overloaded and the output voltage would sag. 



For small load changes the graph shows that the voltage won't vary very much, but at 4\$\times\$ overload you'll be in the higher part of the graph where the voltage will decrease quickly with increasing current. The fans would get too little voltage and due to the limited current won't spin.

If you need 12 V and have 6 V solar panels then placing two of them in series is indeed the right thing to do.