User Mark makes repository A and releases the code under the MIT license with their name in the license. User Jeff forks the repository makes some improvements and adds their name to the license file (still using the MIT license). Then Jeff makes a pull request to Mark's repository. Is it legal for Mark to remove Jeff's name from the license file without reverting the whole pull? If it is necessary to localize it to one country, please tell me the rule for the United States of America.
No, it is not legal to remove the copyright notice of a contributor who has offered a copyrightable contribution under the MIT license. Jeff has offered his work to Mark under the MIT license and Mark must abide by Jeff's license grant in order to legally make use of Jeff's code. If Mark is not interested in preserving the copyright notice as required by Jeff's MIT grant, then Mark has not been afforded rights to reproduce or distribute Jeff's code under any other terms; to do so is a copyright violation.
Socially, it is probably a good idea to bring this to Mark's attention but assume this was done accidentally (merging code can be complex!) until Mark indicates otherwise.
Note that Mark is probably not required to add Jeff's copyright notice if Jeff neglected to add one.
Note also that if Jeff left multiple copyright notices throughout the project, then removing some of Jeff's copyright notices, but keeping a nonzero number of them, is probably a legal grey area. (If Jeff was excessive in adding a wealth of notices, this is a reasonable janitorial task, but this could easily be a malicious, misleading thing for Mark to do under many circumstances; I don't know how a court might rule on any particular set of facts.)
In general, no
You can only copy or make a derivative work of copyright material with permission. That permission is the MIT licence which says:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
Now, if what you used was not a "substantial portion", then you technically don't need to provide the notice. However, you might have to defend that position in court.
Under US law you do not need permission if your use is fair use:
In its most general sense, a fair use is any copying of copyrighted material done for a limited and “transformative” purpose, such as to comment upon, criticize, or parody a copyrighted work.
In the case you describe, this isn't likely to be applicable.
Commonwealth countries have the doctrine of fair dealing which is, in general, less permissive than fair use. Other jurisdictions have broadly similar provisions.