I don't know about deezer, but you cannot download tunes from Tidal. They stay on their servers, you pay a monthly fee, and they stream them to you on demand. With the correct version of Tidal, you will get 16/44.1 aka CD quality data stream and there may be some higher rez formats supported also, but as others have pointed out, often the source material is lower rez and the hi-rez stream is just up-sampled. As far as I know, the way to get CD resolution material onto your NAS is to either buy CDs and rip them, or buy CD quality downloads.
Digital streaming/library
I have purchased a rather substantial 2 channel audio system, and two of the components are a streamer and an audio nas...a melco. I want to build a digital music library. I would love to have the hd level tracks, but the downloads are so expensive. I already have thousands of lps, and thousands of cds. I have iTunes, and it (and rhapsody) allow you to download tracks into your computer...but they are not cd quality. I have a streamer, and I could get the tidal or deezer hi res subscriptions, but do they allow you to download tracks into your computer/nas drive for a digital library?