The MV Editor is released using Qt 5 (http://www.qt.io/developers/) under the LGPL license (http://www.qt.io/FAQ/), it is technically legal to modify the Editor due to that reason alone and the EULA saying otherwise would be in violation of the LGPL. I'm not a legal expert though, and this is just my understanding. I would have to verify that it is released under the LGPL version however, though I haven't been told otherwise. We would need to talk to KDKW to get confirmation.
Nope. The MV Editor is released using the RPG Maker license. The LGPL applies to the QT framework
You will need to deliver the complete source code of Qt (including all modifications you did or applied) to your users/customers.
That means at most, the RPG Maker developers only need to provide the QT source they used, not the editor, and doesn't need to be included with the editor.
The user of your application has to be able to re-link your application against a different or modified version of the Qt library.
Which is the only requirement. eg if I get the QT sources from the RPG Maker developers, recompile it, and then replace the binaries distributed with RPG Maker's Editor, it would still work. This is beyond the capabilities of RPG Maker's target audience, and given that the editor uses QT and Node-Webkit, it would not be enough to re-create the editor. Hence you would not be able to create a Linux editor with just the QT source.
Keep in mind it's entirely possible that the RPG Maker Developers have a commercial license to use QT, and thus they are free to do whatever they want. The Help file includes LGPL license 2.1, but does not indicate which part of the software it applies to.
The "Trademarks and Registered Trademarks" section of the help file isn't specific to the editor or the game client, but if you load up the "credits.html" file included with node-webkit, you'll see most of the same stuff. No mention of QT.
Modifying the player via plugins, or by replacing the node-webkit build is a far less trivial thing.
So there might be a few questions about license that applies to the editor's support libraries, but "modifying the editor" is different from "import/export from the editor, make adjustments outside the editor"
And as I mentioned pages ago, people asking the question of "what would violate the license" is never an innocent question. People ask this question because they have a use in mind that wasn't explicitly spelled out in the EULA.