Does a streamer do anything to the data that Tidal provides?

As long as what they deliver is bitperfect digital output (they should and they nearly always do) there is no sonic impact (nor is there with computers). That is the thing with digital, a bitperfect copy is a bitperfect copy, and you can copy it a thousand times, send it to the other side of the world and back, and it will still be identical.
Personally I do not like the fancy dedicated streamers by audio companies. They nearly always lock you into their dedicated applications, and if there is a service you want and they do not have an app for it, your are out of luck. Here using a small (fanless) computer has definite advantages, and so do streamers like Apple Aiport Express or the Chromecast Audio (my personal favourite). These are by such big companies that no streaming service provider can ignore them. The Chromeast Audio is just $35, and delivers either a good analogue signal through its internal DAC (OK for 16/44, not quite as impressive at higher resolutions, but who streams those?) or a bitperfect optical digital output up to 24/96. What is there not to like?

The only part of CD players that affects the sound is the DAC and just possibly some of the analog circuitry. Bit perfect is bit perfect, and as I said, you can make a thousand generations of identical copies. But you are right about the analogy.

Let me reassure you. I have a few Chromecast Audio streamers, some using the analogue output from the internal DAC, others using the optical digital output. The digital output uses the mini optical connector into the same little slot as the little analogue output does, in the same way some Apple products do. For a test, see here: http://archimago.blogspot.nl/2016/02/measurements-google-chromecast-audio_27.html
The digital output is a relatively unknown feature. I have heard from several people who, like me, were told in a store that the Chromecast Audio only has an analogue output.
On the software side, I am happy with the TuneIn app. It even has a sleeptimer.

Not sure what you want with the ethernet and power plug and why. The Chromecast can use an additonal/optional wired connector if your wifi is not strong enough, and it comes with a power plug (in fact the wired connection uses a special net adapter). What it will not do (unlike the Airport Express) is serve as an additional router to beef up your wifi network (you will need something else for that).
One other difference is that the Chromecast only uses your smartphone or tablet to extablish the connection and as a remote. The actual streaming is done directly from your router to the Chromecast. The downside is that if you want to give it a new command that may take a litle while (and not all apps are very good at this), but the advantage is that it does not need your phone/tablet to actually stream, so youir phone's battery is not drained and you may even turn it off.
Finally, the AE is only 16/44 while the CA goes up to 24/96 (if you care about this).

You are absolutely right. It cannot in any way improve the sound. If it is working properly what comes in will come out in exactly the same bitperfect shape and form.
Of course, if it also includes a DAC (quite a few do) that DAC may influence the sound. But the streamer part is neutral.

I doubt a new DAC will give much better sound quality, if any. If you want better sound I would look at the speakers, as they are responsible for by far the largest part of sound quality (but I don't know what speakers you have). Do you have enough amplifier power (Musical Fidelity has many amplifiers)? What size is the room and does it have a hard acoustic, or not?

@sevs In effect this is a question about which of the two digital volume controls it would be best to use. To be honest I don't know. These days, with DAC's with a 32 bit internal bit depth, digital volume control should not be an issue. Intuitively, I wouold concur with the idea to keep the volume on the Ipad at (near) max, and also on the Chromecast (it also has a software volume control). But this presumes that the Wadia has enough bit depth to do the job (75% is a troublingly modest claim). I wonder if Shadorne can inform this discussion.