What is a masque? Is it like a masquerade? How often did the Nobility throw parties and celebrations?

A masque is a bit more organized than a masquerade, since it involves musicians, singers, dancers, often a written script as well as a musical composition, and a mixture of professional actors and amateur actors from the court up to and including monarchs like Henry VIII, James I, and Louis XIV. They tended to have a combination of aesthetic considerations (the architect Inigo Jones designed some, famous playwrights like Ben Jonson and William Shakespeare wrote them into their plays), political subtext (since the political elites were usually watching if not actively taking part, it was a good opportunity to get a message out), and truly epic levels of debauchery. 

In terms of how often, I couldn’t find any specific figure, but in general as many as they could get away with.