If the whole family's on Android devices, check out Folder Sync on the play store. It's inexpensive, but it might be available to you all under Google's 'family plan' so you only have to buy one copy for all of you.

The simplest way to save all photos is to share folders on your Diskstation, then set FS to sync one-way (phone to SMB) to those.

The simplest way for your phones to 'find' the NAS is to always have the NAS at a particular IP address (AKA 'static IP). You can do this on the NAS or in the DHCP server on your firewall.

BTW/FWIW, assuming you're using a RAID, upgrading to larger discs is stupidly easy and works the same way replacing a failing drive does (pull one out, replace with new, tell NAS to 'repair' the RAID) then do the same with the other drive - your RAID size will 'pop' to the new disc size. Mentioning this as I'd thought 6TB would be plenty of space for 2 people, which turned out to not be the case.

If you're on Amazon Prime, you can backup all your photos to Amazon Photos (unlimited storage for full resolution and raw) using Synology app "Cloud Sync": sync to "Amazon Drive", and they'll all show up in Amazon Photos.

I also use it to sync with S3 (also Amazon storage) and, using the S3 interface, 'sweep' into Glacier (cheapest TB/mo cloud storage out there).

And welcome to Medum!