Translation:It is neither cold nor hot in fall.
In fact it may be the most common way of putting it.
(It's not capitalized either way.)
Not at all. You may be thinking about months of the year. This dictionary entry refers to three of the four seasons, and none are capitalized:
A quick look at any number of authoritative publications with good copy editing shows that seasons aren't typically capitalized in English.
(It may be different in certain special contexts.)
That's true when "neither" is used before the first one. Otherwise it's not that simple:
You said "2 juxtaposed negatives require 'nor' not 'or'" [my emphasis]. I didn't say "nor" couldn't be used without "neither". I simply pointed out that your absolute statement is not born out by analysis. You might want to read the whole article, and reread our previous comments.