Yes; fair use does not exclude any types of works.
No. Legally, since it doesn't fall under the fair use exception, you would need to seek permission to use someone elses material.
Unless it would fall under "fair use" no it is not "okay" to use copyrighted material without permission
Infringement is the use, without permission, of copyrighted material that does not fall under a "fair use" or other exception to copyright law,
While fair use allows for limited use of copyrighted material without permission under certain conditions, it is still recommended to cite sources when using them in your work. Citing sources helps give credit to the original creators and prevents plagiarism, even if your use may fall under fair use guidelines.
Most likely; critique is one of the uses specified as fair in section 107.
If there is no "fair use" exception the only way to legally use copyrighted material is to obtain permision from the rights holder.
Without permission, and assuming it doesn't fall under the "fair use" exception, it would be an infringement of the artists/writers copyright
Copyright law is US Code Title 17, and fair use is section 107 of it.
Cartoons like Robot Chicken often fall under the category of parody, which is considered fair use under copyright law. Parody allows creators to use copyrighted material in a transformative way for commentary or comedic effect without obtaining permission. As long as the use of the copyrighted material is transformative and does not harm the market for the original work, it is likely protected under fair use.
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Under fair use, using copyrighted material for commercial purposes, reproducing the entire work, and causing financial harm to the copyright owner are prohibited.
All cited images in (or on) this (what ever you need it for) are used under the Fair Use Interpretation of Copywrite Laws. All others are used by permission.