Ok lots of options here.
I am assuming your nas is already working, if not respond.
Basically your music is on that external harddrive. And you want that music on the synology. The quickest way would be to plug the harddrive into the synogloy. This assumes the NAS will be able to see the harddrive which will presumably formatted for mac, others can advise here.
If thats not possible then in the side bar of an open window on mac mini, (right click the happy face in the dock and new finder window) will be your synology. Click it. Depending on how its set up it may want some credentials. In here should be the folder structure of your nas.
Now right click happy face again and new window and navigate to your itunes library on the external drive. In this case you probably only want the folder with the music in, not the whole itunes folder.
Drag that music onto synology window and it will copy over. You might want to do it in batches, slower nases have a habit of bumming out half way through a copy.
Once the music is onto the NAS the next step is setting up the express. Its been a while since I did it but the basic premise is plug it in, then launch airport utility in applications>utilities on one of your macs.
Set it up to extend your network if using it as a wireless bridge, but really and ideally you want to have an ethernet cable going into it back to either a switch or your router.
Once set up its just a case of plugging an optical lead into it and your hifi, any mac will now see it as an airplay device.
Now caveat:
This does not represent a particularly good HIFI set up by the way. You have to consider network load if nothing else. There will be those that will argue about sound quality, but network load for you will be a significant issue. Consider how it works:
On your hifi you want to hear music. Launch itunes or what ever player you use on you air, It connects via the network to the nas. You pick some music, that music is then streamed/transferred to your mac from the nas via the router. But you want it out the hifi so you hit airplay, so now the music is nas>router>Mac>Router>Airport
There is opportunity here for things to go wrong and very frequently it will.
My advise is to retain the mac mini. It can be run headless and controlled by the macbook. In this scenario, you pick music on you air, but the mini fetches directly from the nas. You cannot use itunes in this scenario unless you use the very messy screen sharing function but there are far superior players out there that will allow this.
The express can still be installed just for occasional stuff you want off your phone etc.
