Connecting multiple load cells to the same microcontroller
All you need is the following :


Arduino (Mega, if you need alot of inputs.)
Load Cell Amplifier
Load Cells (I recommend only using four wire cells)
Resistors (Only if you are connecting one cell to one amplifier)


If you are using only one load cell per "Scale" , you would connect it as you say correctly. One load cell to each load cell amplifier and then to the Arduino. 

Yes, a single Arduino can in theory take as many scales as the number of Digital inputs you have can provide. You can use the Analog inputs as well but from my experience I would recommend you only use the Digital inputs. You can just share the power and ground sources.

Usually each Load Cell Amplifier will need to use two(2) Digital inputs.

If you want to use multiple load cells together (to improve accuracy) to act as a single scale, you would connect them together in what they call a Quarter, Half or Full Bridge wiring configuration depending on how many you would like working together.

You can write to a DB if you want sure.
What I personally like to do is send the readings to the cloud using dweet.io or ThingSpeak. ThingSpeak.com would probably be best for you.

I usually use the NodeMCU arduino boards that have WiFi built in. They are cheap and work great.

I hope this helps.