The first two, yes. For Compiled Help, the third, I'm sure you know that the files have to be compiled, so no, and I don't think the source files for compilation are a direct export either, unless you can follow an XML path. Although the popularity of CHM is way down from a number of years ago because HTML is more portable, but that's a different issue.
If I were you, I'd look at MIF2go, a Frame add on that does support export to all these formats, and a number of others.
InDesign doesn't do this either...
Just as a word of unasked for advice, choosing your authoring platform by what it can output is a back-asswords way to choose a tool. Find the tool that suits the way you create documents the best so you get more required features to create your stuff quicker and easier.
Both the tools you mention and most other modern ones do pretty open-ended output, either directly or through filters or conversion utilities... there are always ways to massage output to a different format. So output is certainly a consideration, but it's a relatively minor one.
As for input tools, you're comparing apples and oranges with FM and ID. FM excels at book style documents with multiple chapters or files that share common layout characteristics. InDesign excels at shorter documents that are usually design-driven, that require hands-on layout tweaking, and it can't do multiple file management.
Cheers,
Art