Active site residues are the ones directly involved in catalysis, for example, the catalytic triad found in some proteases, e.g., trypsin.  Some biochemists will further differentiate between catalytic residues and binding site residues in the active site, with the latter involved in binding the substrate but not involved directly in the catalytic mechanism.  Passive sites refer to those amino acid residues that do not affect the 3D structure and function of the protein. Some residues, when mutated, will disrupt the global structure of a protein and thus disrupt its function as well, even though they may be far from the active site, e.g., a residue in an alpha helix, which when mutated to another residue, breaks the alpha helix and thus disrupt the function of the protein, albeit indirectly.  Thus those residues cannot be considered passive, as they are critical in the maintenance of the protein's 3D structure, and hence its function as well (because in proteins, function depends on structure).

Generally, residues that ere essential for functional or proper folding are highly conserved throughout evolution, while residues that have little to no effect on function are much more varies. Therefore in the absence of a structure or a reliable model, you can derive some information on the functional importance of each residue from an alignment of orthologous sequences from diverse organims: If any residue is more highly conserved than expected for this type of amino acid, there has to be a reason.

In my opinion you can derive information bu alignmen as Annamarie suggests, thennyou can perform a Circular dichroism of your protein to have informations about its secondary structure, after you can perfomr an Ala scanning of residues more highly conserved and after check mutated protein by dichroism to evaluate if the secondary structure was lost.

This is a complicated questions. First, just to clarify, you are interested in functionally important residues, not simply ones that change an experimentally observable 3D average structure. Functionally important changes include ones that are not evident in by comparing static 3D structures. Residues distant in both sequence and 3D space can be coupled via dynamic networks. Without a 3D structure, sequence and mutant data are your best recourse . For an example of multiple approaches, including sequence covarianc, see http://www.sciencedirect.com/science/article/pii/S2001037016300216. See also http://science.sciencemag.org/content/355/6322/294. The focus of the latter article is 3D structure prediction, but also presents a rigorous statistical analysis that - with reasonably good accuracy - distinguishes residues in direct contact from those indirectly coupled. With a 3D structure available, other methods can be used. See, for example, http://www.nature.com/articles/ncomms6939 , http://www.sciencedirect.com/science/article/pii/S0959440X14000190 and http://www.pnas.org/content/113/17/4735.full.

In some cases, the situation is considerably more complicated. Global dynamics and entropy changes can be fundamental drivers in binding and catalysis. In these situations, the effects of mutations are very difficult to predict by current methods. Some very intricate global mechanisms can be at play. See, for example, http://www.nature.com/nature/journal/v488/n7410/full/nature11271.html and http://science.sciencemag.org/content/355/6322/eaag2355/.

As the late great Rufus Lumry once stated "it is necessary on one hand to expand imagination to envision all the remarkable things nature has been able to do with polypeptides, and on the other hand to convert imagination to truth". - R. Lumry and R.B. Gregory in "the Fluctuationg Enzyme" p. 6 (1986).