Repeating words after "and"

My guess, Doubt, is yes; in fact, you might be able to delete the entire "and that it is"

…it depending on the reference of dangling modifier "it." as it's unclear whether it (that is, "it") refers to an independent variable, a statistic analysis, dietary energy density, or the risk factor

Yes, it can.

Disagree here. If you did that, you would change the meaning.

Should any words be be eliminated?

I don't think so because the sentence means:

A and B were considered independent variables in the statistical analyses, (A) showing that dietary energy density is a risk factor for abdominal obesity and (B showing) that it is associated with low adherence to the Mediterranean diet.