My iPhone12 Pro Max is damaged , how do I back up from unresponsive screen

If the intention is to get to important data on the device not contained in the last backup (recent photos etc.) then a third party data recovery provider might be able to repair enough to perform the backup but your mileage may vary depending on what damage was caused.

You can't. The time to ensure your device is backed and you don't lose data is before catastrophe strikes. It's too late once a device is damaged.

You cannot. You'll need to use an older backup.

If you get the screen replaced it can usually be done without erasing the phone, as long as the phone isn’t already disabled. You have a better chance of success if you take it to Apple.