"Know that no harm can befall you whilst I am here. All I ask is that you remain calm."
-- Gilderoy Lockhart shortly before releasing the Cornish pixies (CS6)
In their first Defense Against the Dark Arts class as second years, Harry and his classmates are tested on minutiae about their new professor. Many students do poorly on this quiz focused on details from Lockhart’s books, but Hermione answers every question correctly. Many students are not taking Lockhart seriously by the time he dramatically introduces the pixies with implications that they are terrifying and vile. However, the Cornish pixies do prove to be a nuisance. They break windows, make a mess, and hoist Neville up by the ears and hang him from a chandelier. When class is over, Lockhart tasks Harry, Ron, and Hermione with rounding up the pixies.
This happened in the afternoon of September 2, 1992. We know that it happened after lunch and the day after the students' arrival at Hogwarts on September 1st.
Going over some of the answers to the quiz, Lockhart reveals that his favorite color is lilac. In the language of flowers, the lilac flower symbolizes the first emotions of love (source: Symbolism Wiki). Such flowers might be used to express the crushes on Lockhart of Hermione and others smitten with the charming celebrity. -BB
Providing the answer to another question on the quiz, Professor Lockhart states that his "ideal birthday gift would be harmony between all magic and non-magic peoples". This seems like a rather contentious and political stance for someone who has based their success as a celebrity on superficiality. Even if it is an odd lie for him to tell, it most likely is just one more of his lies; that sort of wish is quite out of character for someone as self-centered as Gilderoy Lockhart. -BB
Once the pixies are running amok, Professor Lockhart says "they're only pixies" as he tries to encourage his students to catch the little blue creatures. This suggests that, despite trying to make them seem scary moments earlier, Lockhart actually agrees with Seamus that pixies are not much of a threat. -BB
There is obviously some kind of magical power of the pixies involved in them lifting Neville by the ears. No one's ears could actually support their weight.
Unlike a real spell,"Peskipiksi Pesternomi!" comes not from Latin but from English. It would seem that Lockhart is saying English words, but trying to make them sound impressive. The words are "pesky pixie, pester no me." It's not unlike someone trying to sound like they can speak another language when all their doing is talking with a fake accent.