Short answers, pulled from the story.
The First Folio of 1623 grouped Shakespeare's plays into comedies, histories, and tragedies. The comedy section listed fourteen plays, including A Midsummer Night's Dream, Much Ado About Nothing, Twelfth Night, and As You Like It. Two additional quarto comedies, The Two Noble Kinsmen and Pericles, Prince of Tyre, were not included in the Folio but are generally recognised as Shakespeare's own.
The romance category is a modern scholarly label, not one Shakespeare used, applied to his later comedies with a distinctive tone of long separations and improbable recoveries. The plays generally grouped as romances are Cymbeline, Pericles Prince of Tyre, The Tempest, The Two Noble Kinsmen, and The Winter's Tale.
Cymbeline was placed among the tragedies by the First Folio editors John Heminges and Henry Condell in 1623, but modern scholars widely regard it as a comedy, or more specifically as one of Shakespeare's romances. The misclassification reflects how fluid the boundary between comedy and tragedy was in Shakespeare's later work.
Three Shakespeare plays are sometimes referred to as the problem plays: All's Well That Ends Well, Measure for Measure, and The Winter's Tale. The label reflects a sense that these works resist the comfortable resolutions expected of straightforward comic endings.
Seventeen plays are included in the full list of Shakespearean comedies, counting everything from the First Folio's comedy column, the widely accepted Cymbeline, and the two quarto plays, The Two Noble Kinsmen and Pericles, Prince of Tyre, not included in the Folio.
Two comedies were excluded from the First Folio of 1623: The Two Noble Kinsmen and Pericles, Prince of Tyre. Both circulated as quartos and are generally recognised as Shakespeare's own work despite their absence from the collected edition.