Short answers, pulled from the story.
Monet, Renoir, Pissarro, Sisley, Cézanne, Berthe Morisot, and Edgar Degas founded an association to exhibit independently in December 1873. These artists expected to forswear participation in official Salon exhibitions while inviting progressive figures like Eugène Boudin.
The first exhibition occurred in April 1874 at photographer Nadar's studio with thirty participating artists. Claude Monet exhibited a work titled Impression Sunrise during this event which provoked critic Louis Leroy to coin the term Impressionist.
Emperor Napoleon III decreed that the public could judge works rejected by the Salon jury after they refused Manet's The Luncheon on the Grass. This decree allowed the public to view paintings that depicted realistic nudes in contemporary settings rather than historical ones.
Mid-century introduction of premixed paints in tin tubes enabled artists to work more spontaneously both outdoors and indoors. Previously painters ground dry pigment powders with linseed oil stored in animal bladders before synthetic pigments became commercially available in the 19th century.
Berthe Morisot participated seven times while Mary Cassatt appeared four times and Marie Bracquemond three times. Eva Gonzalès did not participate at all despite being one of the four most well known Women Impressionists alongside Morisot, Cassatt, and Bracquemond.