The internet has to come from the ISP's router, right?
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You mean to say modem and you’re saying router. Many times they are in the same box but not always. For instance, I provide my own modem for Comcast instead of using theirs which also has a router and firewall in it.
Not really. Nobody has actually used a "modem" in probably decades.
Yes old school IT pet peeve.
Cable networks still do - you're just bonding a lot of analog carriers together to get the hundreds of megabits of bandwidth. DSL hasn't died out either, and that's also a modem with multiple analogue signals bonded in each direction.
Maybe where you are, however cable has been all digital for quite awhile. in the US pretty much all (if not all) over the air broadcasts these days are fully digital signals, at least IIRC from about 2007.
DSL gets it faster speed by sending a digital signal over the traditional telephone wires. DSL is closer to really slow ethernet than it's old analog dial up cousin.
No, the video is a digital stream, but still carried over analogue channels along with the DOCSIS data. DSL has nothing at all in common with Ethernet, and is multiple analogue channels - IT, DOCSIS (cable modem) and broadcast TV all tend to use QAM, quadrature amplitude modulation, to modulate their datastream onto the carriers. When the manufacturers and standards bodies refer to a "cable modem" or "DSL modem", they are not making a mistake or misusing the term: they really do work by modulating and demodulating carrier signals, just more of them and with much wider bandwidth than PSTN modems used.
Similarly, OTA broadcasts are a digital data stream - but carried over analogue signals at the bottom of the stack.
Mediacom here are just switching from bare digital data streams to digital video over IP, and from DOCSIS 3.0 to 3.1 (fewer wider channels and better noise resistance), as it happens.
Apart from the simplest electrical or optical point to point link, you don't really get a bare digital signal in real electronics. Read the "Operation" section here, which gives quite a good description of how DSL distributes the data flow across the multiple analogue channels to adapt to noise: https://en.m.wikipedia.org/wiki/Digital_subscriber_line
(ETA: not me who's down voting you BTW!)