Different phases on different components
Would I blow my whole setup if I connect the two systems on different phases by connecting them using an Ethernet cable?


No. Computers have isolating power supplies. The logic circuits (motherboard, etc) are not directly connected to the mains.

Isolation is provided by a transformer - usually as part of a switched mode power supply.



Figure 1. A simplified schematic of a switched-mode power supply (SMPS). Source: SMPS.us.

Note the transformer in the DC-DC converter section on the right. The transformer symbol represents two coils wound on a ferrite cord. The windings are insulated from each other and so there is no direct connection between the AC line on the left and the DC outputs on the right.


  Is this setup correct and will work or all devices in a network should be connected via a single phase.


All devices will be fine for the reasons given above.