They aren’t perfect but along with Novation I think they are among the best controllers you can get. But not everyone loves them.
Venus Theory has the same one I do and he keeps going back to it despite owning many others. BTW, his channel is a really good one for making and producing music, IMO, in that he goes a lot more in to the philosophy of things; really interesting.
I think it’s more that there’s a set of price and functionality tiers. Some people prefer mini keys to full size, and others the opposite; other times, there’s additional functionality as a differentiator. One example for functionality is the difference between things like the Arturia Keystep and the Keylab, where the Keystep has a lot of functionality built in around sequencing, arpeggiating, and controlling hardware synths via CV outs. Meanwhile the Keylab is all about providing a full size keyboard and knobs/pads/etc for MIDI control of synths, often software ones in the DAW.
Then as you note there’s the digital pianos filling their role, and the straight up traditional synthesizers. These exist at many price and functionality levels too.
Then there’s the Arranger Keyboards; these are keyboards with either synth or sample based flows and a ton of built in accompaniment instruments, basically a band in them to accompany you while playing them. Basically think that these are for solo performers/composers that want a canned backing band. I always think of Lounge singers when I see these, but that’s not fair 
Actually very often they do not, the controllers are superior. Case in point was Korg’s flagship digital synths over the last few years - the WaveState, OpSix, and Modwave - all od which had garbage keyboards.
But again, not all controllers are created equal. A high end Novation is likely going to be a much nicer keyboard than many synths ship with, and many other MIDI controllers. Same for Arturia.
This is actually an option on many if not most synthesizers. In fact the module/rack versions probably account for most of the sales in some cases. Case in point, the Korgs I was just slandering all have excellent module versions:
incidentally those three Korgs are all fantastic synthesizers, I was tempted to buy a Modwave; it’s just they had not super good keybeds for some reason.
No, generally we will die on this hill 
They might be riffing on Native Instruments’ naming scheme there.
Yes, you would need a MIDI interface, as it does not appear to have USB MIDI.
It looks like a nice digital piano, more of a standalone instrument than a controller, but you could use it as a controller too. I think a dedicated MIDI controller would be a better choice for a controller but it all depends on what you want.
I don’t know too much about this one. This will probably greatly surprise people here but I am not generally a fan of Yamaha synthesizers, with many reasons for this all going back to initial trauma from the DX7.
Basically the way I would think about this:
Do you primarily want to have a single master keyboard to control a mix of other instruments (in software and/or hardware?) If so, get a MIDI controller.
Do you primarily want a standalone digital piano to record, with occasional control of other instruments? If so, get a digital piano with MIDI.
Do you primarily want a very expensive hobby that takes up a lot of space but gives you a large number of keyboards to choose from, but brings a nightmare of control and audio routing with it? If so, start collecting hardware synths with keyboards 
I find a single MIDI controller to be the most flexible; with it I can control a lot of other MIDI soft and hardware synths as needed. I’m never going to be Jordan Rudess up on stage surrounded by many synth keyboards (incidentally he has a youtube channel too
)
@wellbi and @g13dip can keep me honest here in case they disagree or I missed anything big.