(My guess: as the -chen ending is used to signify that it is a smaller version of the stem of the word, this takes precedence over the gender of the stem - and then some German at some point decided that such smaller items were neuters and be done with it.)
I happen to be Norwegian, by the way - and Dutch happens to be quite fascinating in that there are enough similarities with Norwegian and German for me to be able to read Dutch well enough to understand what is going on - I’d never read a novel in Dutch, but newspapers are fair game.
It's really fascinating that you're able to understand Dutch newspapers though! Despite knowing quite some German as well, Norwegian doesn't really make a lot of sense to me. I can correctly guess some Swedish (which I seem to recall is similar?) words when written down some of the time, but far from often enough to be able to follow newspaper articles.
No. As a native speaker, I would consider "die Fräulein" incorrect in the singular. "Die Fräulein" is the correct plural of "das Fräulein", however.
Regardless, at least in Germany, "Fräulein" is considered archaic, bordering on offensive.
Yes, that's true. Roughly speaking, little and cute means neuter. [1]
To confuse you even more, however, note that "die Mädchen" is still correct, but for an entirely different reason: It means plural! ("the girls"), because it happens that the plural of "Mädchen" is the same word "Mädchen", and that the plural neuter noun marker "die" is exactly the same as the sigular female noun marker "die". (Moreover, also the male and female plural noun marker is "die".)
[1] Now that I think more if it, that's quite progressive in terms of gender-equal language and early childhood. (But many other aspects of the German language aren't, so don't expect too much here.)