Para Aduma is the חוקת כל התורה כולה the ideal way for a yid to live is on the levels of oneness with Hashem called חקיקה engraved. The aspects of Para Aduma develop this philosophy further: 1) Aish and (living) Water are a Keili when all else is purged and the essence alone remains you’re left with just Ohr (the living, eternal waters) 2) Learn from Shlomo HaMelech אמרתי אחכמה והיא רחוקה ממני doesn’t mean he tries to understand and failed, but, rather that he tried to incorporate the essence חוקת התורה with his mind and heart אמרתי אחכמה and succeeded but the חוקה was still more than the אחכמה, it was רחוקה. 3) because of the idea that מתוך (the inner side of) שלא לשמה בא לשמה (is the לשמה itself) we are all holding there on some level and in some way.
