What do X-ray diffraction and NMR tell about the Proteins?
Dynamics can mean many things, and not all proteins undergo extensive conformational changes during their lifetime. Some are fairly rigid in solution. 

XRD or NMR data represents an average over the conformations of a protein construct sampled under experimental conditions. A protein construct is a variant of the protein, selected to allow expression and purification, and possibly also to ensure stability and crystallization (as necessary for XRD). 

NMR or XRD data is processed to derive an ensemble of geometries that are consistent with the data and satisfy other criteria, usually imposed by a protein force field or prior statistics about the frequency of geometric features, which allows scoring the quality of a geometry. Before being deposited, the ensemble undergoes quality control by the PDB, amongst other things to verify that there are not too many or extreme violations of expected protein geometric parameters (bond lengths, angles, dihedrals, vdw contacts). Deposited NMR geometries are intended as representative, not exhaustive.

Whether experimental geometries are relevant depends both on the protein and what structural (or dynamical) questions are of concern. Approximating physiological conditions improves the likelihood that the data is relevant. 

Proteins under XRD have less conformational freedom, they are more "rigid" (having looked up the definition in Meriam-Webster's dictionary) than those in solution. Different XRD samples (crystals) may still capture views of significantly different conformations, and complementary techniques such as NMR can be used to fill in gaps.

Yes, bigger proteins are more difficult generally to study, but progress has been made. Some of the limits are instrumental, others with sample prep. There is no single answer (too broad). Q4 is a standard problem. You get the structure and then worry whether there are inconsistencies with what is known/expected. You can try different media and see if they generate different structures.

Why is crystallizing proteins hard? Crystallization has to happen spontaneously! The protein must be kept stable (folded) as it crystallizes, which means being restricted to a narrow range of solvent and temperature conditions. There's a lot more that can go wrong versus what needs to go right.  Even as you want the protein to associate and form an ordered crystal, you don't want it to form the wrong kind of interactions resulting in a disorderly aggregate.