When writing an academic paper, you must acknowledge all the resources (oral, print or web, including YouTube videos and social media posts) used in your research. Not only does this allow your instructor to locate the sources you mention, it prevents you from being accused of plagiarism. In most instances, plagiarism is unintentional; it can be confusing to know what to cite. In general, it is better to be safe than sorry.
No, even if you don't use the authors' exact words, the ideas still originate with them. You must give them credit.
Yes, it is. You must give credit for any content you copy.
Absolutely. the fact that it is easy to do doesn't make it right. Cite the source!
No, it is not. Even government information must be cited.
No, you do not need to cite information that is considered "common knowledge."
No, it is not. If there is no personal author given, then perhaps there is a corporate author (e.g. Virginia Department of Transportation). If there is no personal or corporate author then, the title will come first in your citation.
No. You should still give credit to the person you're quoting. Use Twitter's Advanced Search to find old tweets!