So many questions...
To start from the bottom: Yes, you can run W10 in Safe Mode with Networking.
The trick is how to get there. Since Win8 they've removed the F8 for startup options. Read on!
When you start your system and see the 4 pane window and the revolving balls, shut your system down by pressing the start button for at least 4 seconds. Repeat. On the third run you should see a message saying they're trying to fix the start issues. You'll then see a Choose an option screen, select Troubleshoot > Advanced options > Startup Settings > Restart. From there on it's quite straightforward.
From the Troubleshoot options you'll also find System Restore, which may allow you to roll back the latest update.
It might also be a matter of too high a refresh rate, in which case you might want to start in Low Resolution Video mode. When there, you can set the resolution to the default in the Display Settings (right click on Desktop). Go to Advanced Display settings, set the resolution, continue to Display Adapter Properties and select the 60 Hz option for the default resolution. If something higher is on by default, that's the issue. I've noticed that especially with Nvidia video cards using a VGA connector. With the correct resolution and refresh rate combination you can then reboot to normal Windows.
Hope that helps.