Short answers, pulled from the story.
Silent Hill: The Arcade is a rail shooter arcade spin-off of the Silent Hill survival horror series, developed by Polygon Magic and published by Konami. It was first revealed at the 2007 Japan Arcade Operator's Union trade show.
Players use light guns to aim and shoot at enemies along a fixed rail, similar to the House of the Dead series. Pointing the gun away from the screen reloads it, and a second player can join at any time as either Eric or Tina.
The two playable characters are Eric and Tina, members of their school's Occult Club in Portland. They enter Silent Hill with four friends named Bill, Jessie, Ryan, and George, who disappear after the group stops at a motel.
The Little Baroness was a steamboat captained by Eric's great-grandfather that vanished on Toluca Lake seventy-five years before the game. It disappeared because a girl named Hanna, thrown overboard by her mother due to a terminal illness, caused the boat and everyone on it to be lost.
The Arcade has at least three endings that vary based on player actions. One sees Eric and Tina rescue Emilie and free Hanna's spirit; another traps them permanently in Silent Hill if Emilie dies and Hanna is not freed; a joke ending sends them into the Gradius video game, shown being played by Robbie the Rabbit.
Emilie is Tina's 9-year-old pen-pal, found wandering Silent Hill while searching for her mother. Her mother had been murdered in a home burglary a year before the game's events and appears as a monster who throws Emilie into Toluca Lake.