Rona Thorne, the blonde movie star and secret Russian sleeper agent from Movie Star (2011), is sitting in the briefing for newly recruited IIA agents; along with computer hacker George Spelvin's two Asian twins henchmen from Tragical History (2011). Also there are Patrick "Crash" MacCaren, the assassin from The Archer Sanction (2015), Mercedes Moreno from Coyote Lovely (2013) and Charles & Rudy who were introduced for the first time in Honeypot (2010).
Cyril says Mandarin is the main language of Singapore. This isn't quite true. There are four official languages; English, Malay, Mandarin, and Tamil. The main language and lingua franca is English (the link language). Singapore was a British colony from 1819-1963.
When Colt grabs items in his apartment he thinks are important is based on the scene in The Jerk (1979) where Navin grabs the items he thinks he needs to survive on his own.
The alien in a bikini on the poster in "Colt's" apartment appeared previously in Archer: 1999 -- Happy Borthday (2019), which is to say it appeared to Archer in a dream while he was in a coma.