1. Is it a property of all quantum gravity theories?
2. Do all string theorists and not just Susskind, Maldacena, t'Hooft, believe HP to be property of string theory?
3. As most prominent basis for Holographic Principle is associated with dependence of Black Hole Entropy on area and not volume, is just that much fact justifiable to include it as property of string theory?

Holographic Principle suggests that matter, space and time are the product of the non-material information. Such a vision needs a new approach in the physics. This change needs also experimental justification and a proper interpretation of the experiments.

The holographic principle manifests itself in string theory in the form of the so-called "AdS/CFT-Correspondence". It was formulated in the late 90's by Juan Maldacena (hence it is also often called "Maldacena Conjecture") and it states a duality between a type IIB string theory on an [itex]AdS_5\times S_5[/itex] and an [itex]N=4[/itex] supersymmetric Yang-Mills theory (which is a conformal field theory, CFT) on the 4-dimensional boundary of the AdS geometry. It consists of some kind of mathematical dictionary which relates quantities (like correlation functions) on the string theory side ("bulk") to quantities on the CFT side ("boundary"). One should emphasize that this is just a conjecture, no rigorous mathematical proof exists so far, but its success has led to the point where most people accept it as a fact. One of its remarkable features is that it relates strong coupling on the boundary to weak coupling in the bulk, allowing for perturbative calculations. This is of great use for describing strong interactions: quark-gluon-plasma, as it appears in heavy-ion-colliders, is one of the main applications of modern holography.

In it's strict mathematical formulation, it is restricted to string theory.

I'm not sure about Susskind and t'Hooft, but Maldacena is the one who conjectured it.

The black hole entropy was derived without explicit use of string theory, and as such it can be seen as a manifestation of the holographic principle that is not part of the AdS/CFT conjecture.

More generally the holographic principle might (stress on might --- this is open research) be really just a manifestation of locality of interaction. In most theories, it can be shown that the entanglement of the ground state is short ranged, and the entanglement entropy follows an area law rather than volume law; this is in contrast to the generic field state which would have long-ranged entanglement and volume-scaling entropy. This suggests that one might employ a variational approach to finding the ground state by restricting attention to states with these characteristics; this is done (successively) in DMRG (where the states are matrix product states) and more generally one can use a more generic MERA (multi-scale entanglement renormalisation ansatz) which allows algebraic decay of correlations as found in relativistic or critical theories. Recasting the variational problem as a minimisation problem gives essentially another field theory, but on a different space; generically on critical (and relativistic theories) you'd expect that space to have the original space as a boundary and a new dimension representing the scale (possibly with some interesting inner topology to account for phase transitions).

The only case where all this is worked out is in the canonical AdS/CFT correspondence of a particular string theory and (supersymmetric) Yang-Mills theory. But various hints exist (e.g. Ising models, Fermi/Luttinger liquids in low dimensions) that it should hold more generally.

If memory serves, PhysicsMonkey should have very intelligent things to say about all this.