jquery is really just an abstraction for dom, it is not an api for application building. When I have to use the dom, I definitely turn to it. I'm not sure why people object to having additional helper functions in jquery for a measely 100k or so.
You don't have to use plugins you know, its not a law.
Whether 100k is huge or not depends on the project's requirements. In some cases it's perfectly fine, in other cases it's a problem. Such a broad statement cannot be supported.
Much the same; even if jQuery is that much slower it can sometimes provide something that overcomes the slowness factor. It varies from project to project. Especially if the project scope practically requires you to rewrite jQuery from scratch, you might as well use it.
100k is huge, period. Whether or not a huge dependency is acceptable depends on the project. Yes, we know it depends on the project, that was the point of the site. The whole point is "if you are making a library, and don't really need jquery, please don't force that extra dependency on users of your library".
You don't have to use plugins you know, its not a law.