Exploration, though, not so much. But you have is "object." and then read the methods and properties. It's not awful, but if you don't know the object first you can't do it.
I would highly suggest using javadoc before something like SO when you are confused about how to use a class. The vast majority of SO's java help is frozen in time due to SO's 'no duplicate questions' policy. Java has improved a lot since java 7.
Re: "introductional/topical contents", this is what package-info.java files are for.
Yes.
> What about finding all symbols in a package?
I do not know what exactly you mean here, but I look for stuff like "all methods" or "implementations" in IDE.
> I use inline IDE documentation a lot but still also use the online or offline copy of the HTML reference manual.
I literally never ever use offline copy of the HTML manual nor need a need for it. I use online copy when google lands me there - but typically I then find the same thing in IDE, because then I see also a source code and have generally great experience.
To me, having to read manual online is a fail of documentation.