In this episode, Logan's suite door is to the right of the elevator. Earlier in the season, the elevator was a room, where Logan and Kendall were staying.
Keith handcuffs himself to Lucky and throws the key down a drain. The sheriff is shown trying multiple keys and having difficulty unlocking the cuffs. They key is clearly visible as it falls down the drain and is a standard, universal handcuff key. Every officer would have had at least one copy of this key on their person.
The Alterna-Prom invite is dated May 13th Friday. However, the episode aired in 2006 and the 13th of May fell on a Saturday.