Fair use (in the united-states which is the only jurisdiction where it applies) is defined by 17 USC 107. It does not matter whether the user is a formal educational institution nor not. It will matter whether the use is educational or not, but that alone will not determine whether a use is a fair use or not. There is no set limit of length below which a use is a fair use. In general the more of the source that is used, the less strong the case for fair use is, but in some cases the use of the entire source can be a fair use, and in others the use of even a small fraction has been held not to be a fair use.
That a use is on a Youtube channel does not determine whether it is a fair use or not.
The Four Factors
The actual law specifying the factors to consider reads:
The fair use of a copyrighted work, including such use by reproduction in copies or phonorecords or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright. In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include—
(1) the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of the copyrighted work.
Court cases have said that no one of these factors is final - each must be considered. Some cases have emphasized one factor, some have emphasized another. In addition the law permits a court to consider other factors, not listed specifically in 17 USC 107.
The factors analyzed
The effect of the factors is, roughly:
Factor (1) favors fair use when the use is for educational purposes. It also favors fair use when the use is not for profit. Note that this is not the same as no fee being charged. Profits made by advertising can also be considered. And a non-profit user may still charge a fee to cover costs.
Factor (2) favors fair use when the original is basically factual, such as a textbook or a news report, and weighs against fair use when the original is a creative work, such as a work of fiction, a poem, or a song.
Factor (3) favors fair use when only a small part of the original is used, and weighs against fair use when much or all of the original is used. There is no absolute standard for how much, either in terms of word count or duration, is allowable.
Factor (4) favors fair use when the actual and potential market for the original is not harmed by the use. It weighs against fair use when the use might tend to reduce the paid market for the original. If an individual use would have only a minimal effect, but if many people were to make similar uses that would have a sizable negative effect on the market, that would weigh against fair use. If there is a potential market that is not being exploited currently, but which the copyright holder might exploit in future, and the use might harm such a potential market, that would weigh against fair use. In the use would tend to substitute for the original, so that people would be less likely to seek out the original, that would weigh against fair use.
Fair use cases often use the term "transformative". A use is transformative when it uses the work is a significantly different way from the original. For example, a poem may be published to cause an emotional effect on the readers. But a poetry text may use the verse as an example of a technique of poetic composition. That would be a transformative use. Being transformative is sometime thought of as a fifth factor, but more often as a way to analyze factor (1). In any case a transformative use is much more likely to be held to be a fair use.
Under current US law, any copyrightable work is protected teh moment it is "fixed in tangible form". This includes bein written down, and beign saved as a computer record, as well as an executed sculpture or pictorial work. (A copyright notice and Registration was required prior to 1978.) This matches the law in almost every other country.
However, one must file for and obtain a certificate of registration before one can file suit in a US court for copyright infringement. In addition, unless one registers a work with the US copyright office before the infringement occurs, or within three months after the work is first published, certain rights under US law are forfeited. Specifically, the right to statutory damages, and the right to costs and attorney fees. Statutory damages can be assessed on proof of infringement, with no need to prove the amount of financial harm done or any profit by the infringer. They can range anywhere from $750 to $30,000 per work infringed, or up to $150,000 if the infringement is found to be "willful". Thus early registration has possible benefits.