Backing up phone with broken screen.

Short of getting the iPhone repaired, no. If there’s an iCloud backup configured and running, that might capture the current contents if enough of the iPhone is still working, but you likely don’t have that iCloud backup configured as you’d probably be asking how to restore that and not this question. Backups need to happen before the damage or loss or theft or failure or corruption.

No. The screen will need input from you (passcode) to open. You'll have to restore using an older backup.

You can certainly try connecting it to a computer and see if you can backup, but it typically won't work.

You need to back it up before something goes catastrophically wrong, not after.