Does backing up my iPhone also back up photos etc?

That would depend on how you are managing photos. If you are using iCloud photos, those are not backed up since they are housed in iCloud. If you are not using iCloud photos and the photos only reside on your iPhone, then yes, they are included in the backup.

...also photos sync'd from a computer are not backed up either.

Yes. All photos saved in your iphone will be backed up when you do the back up.

Depends on what you mean by "saved"

I have 5000 photos on my phone sync'd from my Mac but none are backed up.