[MMM]

3. I'm trying to understand her cultural background in this respect (i.e., her parents never used cutesy nicknames, were more formal, and only used each others' actual names).

Is this abnormal? My parents have never called me by anything but the name they gave me.

4. The reason I'm posting, I'm hoping to get ideas for japanese terms of endearment, romantic petnames and nicknames, etc.

5. If such a practice is rare or unheard of in the context of native japanese culture, then what's the best I can do to use japanese words in the way that americans use certain words to address a romantic interest?

They are not used in the same way as some couples use them in the US. It is really a personal decision between the couple.

I want her to feel like I'm putting her on a pedastal; that I respect her as an equal/superior.

How is putting her on a pedestal making her an equal? Take her off the pedestal.