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I don't know about in your system (I'm not knocking it, I just haven't heard any of those components) but streamers do improve as price increases (not always and not in a direct 1:1 ratio). I don't know if buying something like an Auralic Aries would improve your sound but I'm pretty sure you're not going to get great sound out of a $50 Bluetooth streamer.
I don't have any experience with this particular device but streaming music from the phone using Bluetooth usually does not sound as good as streaming music using a streamer with a built in DAC. That said, my suggestion is to trust your ears. There's always something out there better than what you have....
Regarding your first question, in that scenario the DAC in the speakers will basically override the streamer DAC and is used. Lot of folks including me use a (better) outboard DAC connected to the streamer - with a built in DAC, to get a better sound quality.
As for the second question , remember some folks approach music playback as a hobby and part of the hobby is the ability to tweak, upgrade, etc., and most all in one solutions don't provide that level of pleasure. Case and point is I heard the so called wireless KEF LS-50 speakers for the first time at a friend's house this past Friday night and I was extremely impressed. Probably the simplest system I had ever seen to operate and the sound quality surpassed many if not most of the separates I had heard.