Interesting attempt.  Can't say it made for a very good story, though.

Belldandy has a "western" figure?  Could've fooled me.  I thought this was
Urd until they got to the temple.

The characters on the shops could have been either Chinese or
Japanese, but with this new bit of information I realized that it was
probably, in fact, Japanese (as it turns out, however, it was something
of both- most of the shop signs were Chinese Kanji, or pictograph-like
writing, adopted into the Japanese alphabet).  The people had the slopes
and lines around the eyes and nose that made me realize they were not
Chinese, as I originally thought

The word "kanji" is Japanese; the Chinese word for their alphabet is
"hanxi".  And I would describe it as "one of the three Japanese alphabets"
rather than "adopted into the...".

Also, <begin soapbox>, Japanese and Chinese people can't reliably tell each
other apart until they open their mouths.  There is no difference in 
"slopes and lines around the eyes and nose" consistent enough to use as a
distinguishing feature. <end soapbox>

Akane Tendou-san has placed an ad

In English, this is strange.  Belldandy hasn't explained "san" yet, and
she's using our name order, so she should probably be using a prefactory
"miss".  I hope she does explain Japanese name order before Akane gets
there.

The word for no, in Japanese, is 'iie [ee ay].

I'm a little confused by your pronunciation guide.  Earlier, you used
"ay" to indicate how to pronounce Eigo; here, iie.  The two sounds are
different.  The first syllable of "eigo" is the English long "a"; the
second syllable of "iie" is the English short "e".

The word for 'I' is watashi wa." 

While standard for teaching Americans in America how to speak Japanese,
I don't think this would be, by itself, very useful for teaching
English-speakers _in Japan_, as it leaves too much out.  For instance, very
few
Ranma characters use "watashi" (Shampoo comes to mind).  Almost everybody
uses one of the other words for "I" (Kuno uses "boku"; Ranma uses "ore";
Ukyou uses "uchi"; Akane uses "atashi".)  Also, Belldandy is leaving out
the grammatical role of the "wa" here as the topic marker.

The word for American

The last syllable should be "jin" [jeen].  "Gin" [geen] means "gold".
There shouldn't be any confusion... oh, I see, you're on the vowel sound.
The standard, taught answer is [jeen], but [jin] is probably an acceptable
accent.  Generally, if the Japanese don't distinguish two sounds, then
either sound, or any sound in between, is "heard" (understood) by them to
mean the same.  Think "r" versus "l", which they don't distinguish, or [she]
versus [see].  

The same phenomenon occurs in Americans with regard to vowels; Americans
hear a wide range of sounds as "a", for instance.  People who've studied
the matter can often listen to you and then identify where you grew up
based on the exact sound you make for a short "a" in different words,
but most people can't/don't hear the difference.