I've been asked by my professor to do a research about the characteristics of Theoretical Linguistics, and now I'm stuck.
What are these characteristics that makes theoretical linguistics a scientific study? Please add references when answering.
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The answer to this question very much depends on who's asking and why. And what stage of your linguistic studies you are at.
For the lay person, I'd start with James McCawley's "To ask a professional linguist how many languages they speak is just like asking a doctor how many diseases they have." This pointing to the dual meaning of the word 'linguist' in English but also to the fact that theoretical linguistics is concerned with general principles common to all languages.
It might also be useful to distinguish linguistics from philology - the latter dealing with a description of specific languages and from pedagogic or prescriptive grammar.
The reading I might recommend at this stage is Stephen Pinker's Language Instinct (although I completely disagree with his conclusions, it is a good initial overview).
The definition I would have parroted back to a professor during my undergraduate studies would have been something like: "Theoretical linguistics is characterized by a concern with general principles governing how language works using methods including corpus analysis, contrastive analysis, psycholinguistic experiments, etc.)."
For readings at this stage, I would go to the classics:
And if you wanted to get more in-depth:
But today, I would be more interested in discussing with how various linguists' theoretical preoccupations direct what they study and how. For instance, in order to understand the divide between the Chomskean tradition and the rest of linguistics, theoretical concerns are paramount. Like many social sciences, linguistics has a bit of a science envy, which can lead to overcompensating with formal approaches that obscure more than they reveal.
Some authors who addressed this (off the top of my head):
There are, of course, many more things to read and many more perspectives to consider. This is not just something that can be answered without going into the very foundations of the study of language and that can't (and shouldn't) be done comprehensively on SE. However, we can probably provide a relatively safe starting point.
Theoretical linguistics is scientific because it is based on facts. Language expressions are cited which are proposed to be acceptable, or not acceptable, to native speakers of some language under discussion. Such facts are taken to argue for or against some linguistic theory.
Theoretical linguistics is not a mature science, and there are often, perhaps always, questions about whether the facts are true, whether they are collected in an unbiased way, and, in general, there are lots of methodological problems. And there may also be questions about the coherence or lucidity of the theories. Probably a reasonable case can be made that theoretical linguistics is not good science. But it is based on (purported) facts, as you can easily see by looking at practically any dissertation on theoretical linguistics. So, it is scientific.