My point is that this may indeed be the case! The extra dimensions may be as real as our ordinary 3, although compactified.
No no. We'll try to measure them at LHC.
This sounds more like new age stuff
Remember that all extra dimensions in string theory are spatial.
To start with, all (including the ordinary 3) dimensions are on the same footing. It's just that all but 3 need to be compactified.
Until then, I suggest we call them real.