Is Buddha nature everywhere the same? Is Buddha nature everywhere the same? 

I don't think so, that seems wrong. But original enlightenment is always everywhere bliss, right? So how can Buddha-nature, which I would translate into, rather than "awareness" as the early Korean Son master Chunl's translators do, place, ever be impermanent independent of the body? 

Without rupa, form, "awareness" -- or place -- is presumably just nothingness, unless original enlightenment -- just like enlightenment itself -- can be lost and gained?
Is Buddha nature everywhere the same?


Yes and No. As Najarjuna stated: Neither one nor different (非一非異). 

Also as the Heart Sutra stated: Neither arising nor ceasing, neither defiled nor pure, neither increased nor decreased, therefore formless in Emptiness it is; no Taking, Thinking, Conducting or Cognizing; no eyes, ears, nose, tongue, body or mind; nor vision, sound, smell, taste, touch or phenomena; no dimension of eyes so forth even no dimension of consciousness; no ignorance also no ending of ignorance, so forth even no aging-death or ending of aging-death; no suffering, aggregating, cessation or the path, no wisdom also nor has any attainment. (This supposed is addressing to Śāriputra. But only few understand who or what is "Śāriputra" in the Heart Sutra. Xuanzhang translated it as 舍利子, not 舍利弗, the later is common translation for Śāriputra.) 

Because this "Buddha-nature" is not an object or concept, anything the human mind capable of conceiving is not it. Like you can draw the moon, photograph the moon, look at the moon, but you cannot touch it or hold it in your hand. You might argue that the spaceman can touch the moon. But no. Think about it, he is only touching the moondust. Therefore the teachings can only teach what it is not. 


  Without rupa, form, "awareness" -- or place -- is presumably just nothingness


In the strict sense, we cannot talk about nothingness either. Many talk in our common language as if "nothingness" does really exist - see the mistake? Even the 7th Dhyana the Sphere of Nothingness, that nothingness is just a "pretence" - explaint by ancient meditation teachers in the Sutras. It is a kind of stoppage of mental activity or conceptual proliferation. Hence the Sutra said one died at the 7th Dhyana will be reborn in the Asamjnisattvah Heaven (the heaven without thought) and followed by the stupid animal realm. 

Ultimately, talking about Buddha-nature perhaps a good exercise, but only seeing it gives the real taste.