IANAL but I have discussed this and many similar issues with lawyers enough to have a good idea of what I am talking about here. This is not legal advice. The best background reading is Larry Rosen's book in the context of open source software.
Rights, Licenses, Copyright and Sublicenses
Under copyright law a copyright holder is granted certain exclusive rights over his or her work. Most or all of these (depending on jurisdiction) can be exclusively or nonexclusively licensed to a third party. If sublicensing is allowed, a licensee can pass on some or all of the rights in the license to a third party by contracting directly with them.
Currently in the United States, exclusive licensees are assumed by statute to have a right to sublicense (though I presume this could be further clarified in the exclusive license). This makes sense because exclusive licensees are presumed to have control. Nonexclusive licensees are not assumed to be granted such a monopoly by the licensor.
For example, suppose I write a novel. Suppose I offer an exclusive license to the work in its current form as a book, and I offer someone else a non-exclusive license to make a sequel which is a derivative work. The exclusive licensee can issue non-exclusive licenses to other authors to use excerpts from the book by sublicensing. The non-exclusive licensee cannot authorize yet another unauthorized sequel of my novel, nor can the exclusive licensee sublicense a right they have not been granted (movie rights for example).
BSD vs MIT licenses and Sublicensing: A Possibly Big Difference
This section is mostly based on Rosen's book (above). If you need legal advice, please hire a lawyer, and don't get it off Stack Exchange.
The MIT license explicitly allows sublicensing while the BSD license does not. Following the above discussion this means that the MIT license allows something that the BSD license probably does not in most jurisdictions, namely sublicensing. Both licenses address, however, only the code and software provided and neither one limits what a work as a whole can be licensed under. This leads to a significant question of how to interpret the GPL v3 to be compatible with the BSD licenses btw.
Under the MIT license you can do basically two seemingly similar things:
1) You can incorporate the work in your own works and distribute these under a more restrictive license.
2) You can take the original MIT-licensed work, add additional restrictions on it, and distribute the work under a more restrictive license but where you have not modified the code at all. The GPL v3 claims to require this to be compatible, if one sees the GPL as governing all terms of the license.[1]
Under the BSD family of licenses, however, you can only add restrictions to your own code and to the derivative works you create. You cannot add them to the original code by passing on only some of the rights granted to you. So I can't take the BSD-licensed PostgreSQL, rename it to PostSQL, and license it under the GPL, but I can take MIT-licensed Kerberos and rename it as HadesHound and license it under the GPL (in both cases assuming that no code has changed). This means that the vehicle for rights is different (always direct in the case of the BSD license, either direct or indirect in the case of the MIT license).
Conclusions
Sublicense is a legal term. If you want to read about what it actually means, my recommendation is to start talking with lawyers, the Software Freedom Law Center, and others, and consult legal dictionaries. The basic idea though is that if this is granted, a licensee can become a licensor of some of the rights of the grant they received regardless of any other claim they may have to copyright control over what they distribute.
You are asking about a specific legal document and a term used in it. I hope this helps explain exactly what that term means and what impact it provides.
Many of your questions are likely to be long and complicated,[2] and depend on jurisdiction, but a basic rule regarding the MIT License is that if your channel claims it is licensed now under the GPL, it is licensed under the GPL. This may or may not be a safe assumption under the BSD license however. Moreover this is true regardless of whether the original version was modified or not if the MIT license was used. Under the BSD license, the scope of modifications are indeed determinative regarding which license governs.
[1] One solution is to see the GPL in a different way, and to allow "reasonable legal notices" (additional restrictions under section 7) to include notices of additional license rights. In this case one would have additional permissions which were removable, governed under section 7 as additional permissions, but also allow, as an additional restriction (under section 7(b)), a notice saying that certain rights are not removable. This is one of the things I dislike about the GPL v3, namely that it makes one think like a lawyer regarding how to address license compatibility.
[2] For example there is an open question whether distributing software which links to a third party library requires copyright permission at all. If this is the case that it does, then PostgreSQL compiled on MinGW requires Microsoft's permission and they can revoke that at any time, but if it doesn't then I can write proprietary programs that link against GNU Readline and the FSF can't claim this is copyright infringement. This open question makes most of your questions regarding whether a developer can link to a library under a license other than the GPL impossible to answer with any certainty.
