Backup iPhone without iTunes
Question 1

The activation message doesn't mean it will do a factory restore, no, however it is possible that not all to the data will be retrievable even though you can see it.

Question 2

If you cannot get to the Settings app, which you can't from what you've described, then without activation there is no way to use iCloud to backup. iTunes would be the only option in this case.

Do you have an iCloud backup by chance?