as long as you realize these numbers are used much more for descriptive purposes than anything else. besides, if you have all of the ‘population’, even if it is small, in a sense you have the ‘parameters’ (<— which is still debatable and i would probably argue that even if you get all the units of analysis you’ll never have the ‘population’, but that’s another story).
Of course. The assumptions necessary for multiple (linear) regression do not include scale, number of cases, or origin of those cases. Your question is like asking whether you can draw a graph? This is really all you are doing – describing your data in a certain way. It is not a test of anything, just a way of looking at the results.
Also of course, you must ignore anything to do with significance or random sampling when creating your model – including asterisks and p-values. These are absurd always, but obviously make no sense with census data. So also make sure that SPSS (or whatever) is not using p-values behind the scenes to reject or retain predictors. You will get effect sizes (both R and coefficients). Use these instead.
Using a population makes things much easier (since sampling variation is not an option to explain results). Be humble in your claims since N is small, and tiny in relation to the number of variables.