Is the citation of sources (secondary sources specifically) reserved to "academic writing" or do the same rules apply to other mediums of debate such as oral debates and mooting? Also, how would you cite sources in an oral debate? I haven't been able to find information about this anywhere. Watching oral debates the people involved seem to have all these ideas that surely must have come from a lot of research and cannot be all their original thinking, yet they are able to get away without citing there sources. Is it a rule that citing secondary sources is not necessary in oral debates? Thanks in advance.
The conventions certainly seem different between oral debates and academic writing.
There's no single convention for oral debates. A televised debate between politicians is run quite differently from a university debate between two invited guests on a contentious topic, or from an official university debate competition that follow parliamentary rules. Example:
"One major difference between the use of information in cross-examination debate and in parliamentary debate involves the reliance on published sources of information. Both before the debate and during the debate, cross-examination debaters rely almost exclusively on published sources. Beginning with the extensive research already mentioned, published information is the sine qua non of cross-examination debate. During the debate, cross-examination debaters are required to cite the source of every bit of information they use."
Any debate relies on a lot of research and consultation with sources prior to the debate. Debaters may want to cite sources explicitly to help support their case, and if they don't they still need to be able to back up their claims if challenged in cross-examination, or (often with political debates) after the fact, since the audience and the media will fact-check their statements.
In informal debates the authority of the speaker can often stand as citation enough, if they're speaking on a topic about which they're recognized as an authority. But one reason why they can do this is because it's understood that an expert could produce references if asked.
The basic principles of citation and plagiarism apply equally to oral debates and academic writing, in the sense that if you're using someone's words or ideas without citing, it can hurt your credibility. But the standards for citation vary widely across academia too (historically, between disciplines, between journal articles and books, between writing for academic peers versus writing for a general audience, etc.). It shouldn't be surprising that it varies in oral debates as well.
So I guess the answer is that it depends quite a bit on context.
Hope this is helpful!