Earlier quoted context omitted.
I think "gaining half a bit of information" about something can correspond to stuff that lets you update your probability distribution about it? I'm not sure.
yes, but your gain is still an integer number. the non-integer ratio is just a statistic (gain per number of units).
which they aren't.
if you have a data storage thingy that can store any of three values, a ternary digit, it is exactly equivalent to log2(3) = ln(3) / ln(2) ~= 1.585 bits.
kind of like US pop-science articles like to say stuff like "a volume 1.5 olympic-size swimming pools" (because a megagallon is just weird), even though obviously, can never have half of such a pool or it would empty.
(ok after some consideration, you could have the bottom half)