In the second part of your question, the two different introductory phrases, "aside from the fact" and "regardless of the fact" are both possible, but they mean different things. Aside means that we are consciously disregarding the fact. As a matter of business or logic or whatever our interests are, we have decided to set that matter aside, to ignore it. Regardless means that we don't even care that they are good at X. If it were, say, a discussion about a business deal, "regardless of..." would mean that we will move forward whether they are good at X or not. In this second example, we are not exactly ignoring the matter. Rather, we have addressed the matter and decided that it was not relevant.
Perhaps this will further clarify the difference. With "aside", the sentence is hypothetical. We set aside the issue so that we can discuss matters without regard to that fact. With "regardless" we have addressed the issue, as I said above. It is no longer hypothetical.
Thus, both are correct and make sense, but they have slightly different meanings.