Yes, indeed 
I still think that the person changing has something to do with it. The sound isnāt changing, the person twiddling the knob is - bur we mis-identify the source of the percieved change - as something coming from outside, when the change is actually (only) happening in the mind.
absolutely not, you can even test that yourself by rendering the same ( neutral ) sound from each daw and then phase cancel them
A lot of people on Gearslutz swear by the sound of Harrison Mixbus. I downloaded copy when they did one of their sales and I payed I think 29,- for it but sadly it has just been collecting space on my hard driveā¦
My understanding is that Mixbus used to be special when it was the only game in town that could do inter-channel plugin communication to simulate a mixing desk in front of you where the channels push and pull on each other. Inter-channel plugin communication from VST to VST is still rare, but itās happening from third parties now so it doesnāt need to be a DAW feature so much any more. Airwindows console 5 I think is their latest, and it really does a good job of doing some light saturation and some non-linear summing on busses where whatās happening on one channel can have an effect on all the others.
Brief primer on inter-channel communication: Most console emulators simulate a single channel in isolation, but then when you overload the adjacent channel, nothing happens. With inter-channel plugin communication, the overload of one buss can saturate others as well, etc.
All DAWs are identical. Itās all about the processing you apply. Effects, different instruments will sound different, dIfferent limiters do different thingsā¦ Some of stuff has their own unique perks. But if youāre messing with audio files only thereās 0 difference. Bounce the same audio in each DAW, invert phase of one bounce then play it at the same time with another that came from a different DAW. No sound? Audio files are identical, repeat this with every DAW to find āthatā difference which doesnāt even exist.
Probably the most forward-looking example is Izotope with the masking meter from channel to channel and the visual mixer on the master outs of a mix, not using it to do better analogue saturation at all. I have no idea what Slate does, but I think there is a lot of unexplored potential in this kind of thing.
Yes, this. Whether they sound different or not is entirely irrelevant if youāre working with the DAW that suits your style and workflow.
At the same time i can use power of Reaper and have amazing sound of FL Studio. Nice! 
Most people do the opposite because they sound the same and itās easier to mix in Reaper than FL, but I think you know how to have fun in the studio and thatās what counts 