Are many new math results first published in monographs? Are many new math results first published in monographs (not in articles)?
Research monographs in mathematics certainly exist, but they aren't the standard form of publication.  They are generally not as prestigious as papers in strong mainstream journals, they may be less widely read, and they may be viewed as being less carefully refereed.  Some important work in mathematics has first been published in monograph form, but I wouldn't recommend it unless you have a very good reason (for example, extremely long proofs, or lots of valuable material that would be harder to understand or appreciate out of context).

There are some journals that publish extremely long papers in monograph form, such as Memoirs of the American Mathematical Society.  If you want to publish a research monograph in mathematics, a series like this is a reasonable place for it, while a stand-alone book is riskier.