The answer to this question is already partially in the question: Picasso wanted to show show the horrors of the war, as experienced by the civil population, to the world. He wanted to show that war has devastating effects and by this turn people's opinions against the war.
The bombing was also done by the fascists so the painting can be seen as a symbol for the fights against the fascists.
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The nickelodeon was a type of indoor exhibition space that was dedicated to showing projected motion pictures. These can be considered the beginnings of cinemas. Nickelodeons were cheap (they charged a nickel) and were particularly popular in the early and mid 1900s. This was due to several advantages.
First of all, nickelodeons were very affordable, which made them appealing to a wide audience. This came at a time when the urban middle class was rising. Moreover, these theatres offered a continuous selection of short films, which meant that they provided leisure activities at almost any time. The owners relied on "film exchanges" to have access to a wide variety of new films. This meant that the same audiences would keep coming back, as the content provided was new. This was a great advantage to the patron.
Good afternoon :D
Even though its totally not midnight ;)
Goodbye!