The AppleIGB driver is the one that crashes a lot. It's caused the crash in your left screen shot. It is the driver for one of the Ethernet ports. It sometimes crashes during startup, preventing the system from starting, and sometimes crashes during use. I'm assuming that's responsible for many of the problems you're reporting. I stopped using it because it was too unreliable (you can just remove the kext from your CLOVER/kexts/... directory or from /Library/Extensions, wherever you installed it).
To use the other Ethernet port, which doesn't have the same problems, you should download either the latest AppleIntelE1000e or IntelMausiEthernet driver from the downloads section and install that (the version installed by MultiBeast 8.0.1 doesn't work, but the next release of MultiBeast will install a version that works for Skylake boards). That should activate the other port.
Most non-Apple drivers (FakeSMC, Ethernet/Audio, USB, etc.) are not digitally signed, which is why you get the invalid signature messages when you run kextcache. They will never go away. Depending on how you install things you can reduce the number of complaints (possibly down to only one), but not completely eliminate them if you want all your hardware to work.