Is it a bad idea to ask professors questions weeks before the class starts?
Would it be a bad idea to send an email with questions about the material before the class actually starts?

First of all, I don’t mean to sound harsh, but generally it’s a bad idea to be a person who asks disingenuous questions not because they want to know the answers to those questions but “to show [someone] that they are motivated” and because they “would like to develop a bit of a relationship” with the other person. It’s dishonest, and the thing about this type of dishonesty is, the people the dishonesty is directed at are almost always better at detecting it than the dishonest person thinks. So this approach tends to not produce the desired outcome, and can sometimes backfire in unpleasant ways. And more specifically, most professors have had the experience of having a student try to impress them in various ways that come across as insincere. It leaves a bad taste, which does not help a while later when the student conveniently shows up asking for a letter of recommendation.
Setting this aside, if you have questions you genuinely want to know the answers to, there’s nothing inappropriate about emailing the professor. Professors often enjoy discussing course topics with students and answering their questions. If your questions sound sincere and not like something you contrived just to show that you have something to ask, I’m sure the professor won’t be offended by your email, and there’s a good chance that she’ll answer it. Whether she will like you more as a result or not, I don’t think anyone here can predict, so again, if that’s your true motivation then yes, it’s probably a bad idea to send the email.