Question #1
Smaller sensored cameras have deeper DOF ..because ??
It's simply matter of the physics, of geometric optics - i.e. the 'lens equation' in combination with the geometry of the lens aperture.
The physics and maths is really beyond brief forum discussion here.
Nevertheless, the general rule to remember, is that the ratio between two different sensor/film sizes, linear (not area), gives the number of 'F-stops' required to produce the same DOF, for the same angle of view and same subject distance.
APSC have deeper DOF than FF??
Yes - although not dramatically.
As an example of what I stated above...
35mm FF sensor diagonal = 43.3 mm
APS-C sensor diagonal = 28 mm (typical)
Ratio = 1.54 x (approx)
So the 35mm FF will produce the same DOF when its lens aperture is stopped down about a 'half stop' more than the APS-C camera's lens.
Would a FF camera be able to replicate the deeper DOF of smaller sensors
via smaller F stop choice ..or does diffraction kill this as a viable option??
Diffraction will become an issue if the required physical aperture is small - but that depends on how much DOF you are trying to replicate.
You may actually run out of aperture range with some comparisons.
For example - a 2/3rds inch sensor, such as in the X10 or XS-1, has a sensor dimension size of about 1/4 of a 35mm FF camera (11mm versus 43.3mm) - so if you were trying to replicate the smaller sensors' DOF at F11, then the 35mm FF camera's lens would need an aperture setting '4-stops' higher, i.e. 'F44', to match DOF (which may not be available).
How do FF cams manage to capture deep DOFs in landscape shots which they appear to be able to do ? F stop choice alone ?
Well, landscape shots tend to require 'acceptable focus' from infinity downward - and in this case the DOF is somewhat less of an issue.
Lack of DOF is most apparent with longer focal lengths (i.e 'telephoto'), or closer focus distance.
'Landscape' photography tends to be done more often with shorter focal length lenses ('wide/normal angle' lenses), and greater focus distances - so this makes it somewhat easier to achieve greater DOF - but that's not to say that smaller aperture aren't still required too (depending on the FL used and the DOF required).
I know plenty about it - as I'm not just a keen photographer, but a physicist/engineer too - and just to satisfy my own curiosity, I've even programmed my own DOF calculator, with my own formulae from 'first principles'...