自
=
丶
+
目
:
Mnemonic symbol: a hand mirror, which someone uses to look at themselves.
The Eye of Providence (目) is looking at itself (自) in a handheld mirror (自) in the space station's bathroom (Ø4). It think it's indeed looking very good, since Zorro (z) attached a petal (丶) to its eye (目).
由
=
丨
+
曰
:
Mnemonic symbol: 自由古巴, a cuba libre. The character 由 itself even looks like a cuba libre.
Maud Younger (y) is taking part in a charity auction in the outhouse's kitchen (ou2). She is auctioning the dinosaur bone (丨) next to her and is speaking into a microphone (曰). In the other hand she is holding a cuba libre (由), and she is already quite drunk.
(bound form) base; foundation / (bound form) radical (chemistry) / (bound form) gay (loanword from English into Cantonese, Jyutping: gei1, followed by orthographic borrowing from Cantonese)
基
=
其
+
土
:
Joan of Arc (ji) has to repair the watchtower (其) In front of the space station (Ø1). The tower needs a new foundation (基), and because it is floating in outer space, Joan of Arc can just add some dirt (土) to its base (基) to create a new foundation.