Recover Photos from user partition - unrooted HTC M8 MM 6
To answer your questions in order:

4) not currently.

5) no, TWRP itself does not lose your data. Flashing on locked bootloaders does.

6) not currently. Pt. 2) You do not have to unlock bootloader to install TWRP. You can also flash it via su dd after you root.

7) impossible, at least with SDK. If you know a JTAG specialist or an FBI tech person who owes you a favor, they might be able to recover your photos.

8) no, you are not screwed. There are a few recommendations below, and no, rooting won't "badly overwrite" your data.

Because I know how important photos are, I would suggest:

Option A: Since your photos are already deleted, you might as well unlock the bootloader and root. Unlocking and rooting shouldn't physically overwrite the sectors of the /data partition. (If they were important, life-changing photos I wouldn't have the balls to do this IMO.)

Option B: Buy your wife a new phone (same phone, different phone) and put the M8 in a drawer for about a year. By then, there should be one-click-root apk's for MM, or something better than that, where you won't need to wipe the device again.

Additional reading: Why unlocking bootloaders wipe the device - Android Enthusiasts