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For the NIC3 of VM1, you had better use another static ip address instead of 192.168.13.1, becuase 192.168.13.1 is preserved for the virutal adapter installed on the host platform. You can try to change another static ip address and disconnect the connection of NIC1/NIC2, then try to ping from VM2 to VM1, that would identify if the un-able ping would be caused by the route-table of VM1.
Regards to VM2/3 to external network such as google. Host-only segment do not provide network connection to external network. You can use bridge or NAT segment
I don't understand why with todays technology people use static IP addresses. I understand why people want an IP address to remain constant but this can still be achieved via DHCP. All you need to do is once the IP addresses have been allocated is to tell the DHCP server to permanently associate these address with the MAC addresses.
Some people may not HAVE DHCP servers on their network, or parts of their network. Also, in manufacturing environments and control systems, you want to absolutely positively ensure your devices maintain the same static IP address, as the computers which communicate with them MUST be defined with an absolute address with which to communicate! Don't assume everyone has the same scenario as you are used to.