Is it okay to connect 80 LEDs parallel or in series in pair of 10 LEDs per pair?
You cannot connect the supply in series for these devices. Your -12 V signal is actually Gnd for both supply and the data signal.

You can run multiple +12 V wires to groups of 10 along with multiple Gnd wires to groups of ten. This will reduce the voltage drop or allow thinner wires to be used.
The data signal however needs to run serially through every device if you want to individually address each LED. 

I think that is what you have tried to show in your diagram, and if so then it would work. 

Look at the datsheet for the WS2811 IC.