IPhone – What’s the best way to recover data from corrupted iPhone 6s (iTunes not working/iCloud not used)

You will find that TimeMachine is generally inclusive as far as selecting data to back up. If you take a stock TimeMachine configuration and don't omit anything (supposing your disk is large enough) you will be able to

• Perform the backup
• Remove the backup disk
• Wipe the disk
• Reinstall the OS
• Reattach the backup disk
• Reboot

And all should go smoothly. In the initial configuration dialog on rebooting, you will find a page that asks you if you want to migrate your data, of which one of the options will be from a TM backup. This will result in a very cleanly migrated system with very little changed as far as the individual user goes.

But your question was more specific: Are there data files that you should specifically opt-in for a Mac Backup? Yes.

• Applications folder

  Prior to TimeMachine, I would always kick myself for forgetting the /Applications folder in my backups. Mac apps generally don't modify items in sub-directories of the Applications folder, so if you're trying to get out of a potential corrupted Application, there's little to be concerned of. TimeMachine by default includes this.

• Application Support/Preferences

  Varying heavily from application to application, but generally, most applications look to the ~/Library/Preferences/ and ~/Library/Application Support/ folders for configuration and "temporary" files. This will accomodate #3 on your list. TimeMachine by default includes this.

You will likely find that TimeMachine is very capable as a method to make a non-bootable shadow copy for archiving purposes. If you use it, you should have no issues retrieving any old data ex-post (barring external forces like a bad drive etc.)

Yes. I've done this many times.

The iCloud restore process deposits the sandboxed saved application data, but not the application package itself.

As a second step, you can sign into the store to re-download the apps (or connect to iTunes to transfer the apps) so that it matches the data, but I see no reason why you can't get at the data using whatever tool can read the filesystem such as a jailbreak or PhoneView.