First to point out the obvious..
VMware Fusion 10.x is not supported on macOS Catalina, macOS Catalina support was added to VMware Fusion 11.5.
VMware Fusion 10 is end of life ( https://www.vmware.com/content/dam/digitalmarketing/vmware/en/pdf/support/product-lifecycle-matrix.pdf )
With that out of the way..
For your host Internet problem I would try to uninstall - then reboot your host - then re-install VMware Fusion.
For the black screen issue and VMware Fusion 10.x see this topic:
Wil| Author of Vimalin. The virtual machine Backup app for VMware Desktop Products
| Vimalin : Automated backups for VMware Fusion and VMware Workstation Professional
| More info at https://www.vimalin.com
| Twitter @wilva
| VMware Wiki at http://www.vi-toolkit.com