About the "That EFE is specifically for 4 dimensions.". Does it mean whenever there are 4 dimensions, there is automatically GR?
No. Mathematically, you can have 4-dimensional manifolds that don't even have a metric.
what would change if the world is 4D but doesn't have Equivalence principle and if you put feather and iron core, they don't fall at same time?
Such questions are meaningless unless you give us a specific alternative theoretical model to GR to use when answering them.
In LQG, there is always the comment it can't recreate GR.
This tells us nothing without a specific reference.
Is it possible Quantum Mechanics lives not in the 4D spacetime of GR but it has its own space where time is different?
This is personal speculation and is off topic for this forum.
All this is to prepare for reading Julian Barbour new book "The Janus Point"
If you want to discuss one of Barbour's models, you need to look at his peer-reviewed papers and start a separate thread on one of them.