Since Open Camera is functioning properly, I would follow JohanF’s advice and check out the 0-byte files problem, which seems to affect the default standard Camera app only.
If that turns out to be the case, and you see 0-byte files in DCIM, then two options would be available to you. Either you re-install the .apk as per cited method, or you “just” make sure that your phone’s ROM is up to date, you make sure you have adequate backups and then you do a factory reset
No, I would not recommend using a SD card for the moment.