Wow! I never knew this before.
Getting 100 characters high instead of 25 is the hard part; apparently there's a little-known byte you can tweak someplace to change the character cell height. This is of little use normally, since with a height less than about 7 you could never read the text, so it's seldom mentioned or discussed, but there you go.
Indeed, because you can not change the font. However, that register must be set to 1 to get the normal graphics modes.
As the CGA adapter has 16_000 bytes of on-board ram, you have just enough for a 160x50 character text mode, so again this is possible. (I should have done the calculation before: if CGA supported it as native graphics mode, the resolution could have been 320x100 so as to fill all the available memory.)
Also I guess you have to turn off blinking so that you can have all 16 colors as background, but CGA does have this feature.
Indeed, now that I re-read this manual (yes, I am cheating), I've found this note on the page describing the mode register: "The low resolution (160 by 100) mode requires special programming and is set up as the 40 by 25 alphanumeric mode."