Thanks for posting to the Fusion Community! I'm sorry to hear about the troubles with Fusion 360.
I'm not seeing any issues with our services currently. You can review the status on the health dashboard.
https://health.autodesk.com/
The below link applies to the first error message.
https://knowledge.autodesk.com/support/fusion-360/troubleshooting/caas/sfdcarticles/sfdcarticles/Una...
The error message "Unable to setup Fusion 360 for your Autodesk Account" and the error message "Sign In Failure There was an error while logging into Fusion 360" suggest that this is most likely a network related issue.
Fusion 360 requires access to the list of domains and ports in the below link.
https://knowledge.autodesk.com/support/a360/troubleshooting/caas/sfdcarticles/sfdcarticles/Network-C...
Do you know if there would be any issue on your network that would prevent access to those domains or ports?
There's lots of suggestions in the below link that may be able to help resolve the issue.
https://knowledge.autodesk.com/support/fusion-360/troubleshooting/caas/sfdcarticles/sfdcarticles/Fus...
If you share the Application Log files and the Web Services log files, see the below link with me. I can review them to see if there is anything mores specific to suggest here.
https://knowledge.autodesk.com/support/fusion-360/troubleshooting/caas/sfdcarticles/sfdcarticles/How...
You should double check that the time and date, daylight savings time, and time zone settings are correct on your computer. Sometimes this can cause an issue as well.
I hope this helps. Let me know if you have any questions.
Thanks,
Nathan Chandler
Principal Specialist