What are the coil voltage ratings on your contactors? Looks like you are driving the contactors with 120VAC. If the coils are rated differently, buzzing is typical. And, can you post the schematic of the design.
This is a 50 amp back to back electric brewery panel from kal. All I did was unhook the main plug wires and ran 6/3 in . As you can see, the 2 wire nuts are the neutral and ground tied in and the main power to the contactor. Black and red.
I dont know how that 7 amp fuse connects into the circuit, but is is possible you have one of the hot wires and neutral wire backwards back at the source? That might explain why the fuse blows and GFCI trips. Again, not sure how it all wires together so Im guessing a bit here. Do you have a circuit diagram you could post?
Id definitely check your wiring back at the source panel. If a hot and neutral are reversed, youd have 240v across the contactor coil, and it is only a 120v coil. 240 across the smaller hot bus to neutral bus would blow that 7 amp fuse too. Im assuming your GFCI is a breaker in your source panel; if the wiring is messed up there, I could see it tripping too.
i'm with frobozz. nothing in the photo would indicate a problem, given that it worked totally fine when plug-connected. check the wiring at the source.