La volpe a cui pensavo ieri è proprio simile a quella dipinta nel murale.

“Cui” is the relative pronoun for “whom/which,” and when a verb requires a preposition, the relative pronoun inherits it. Since pensare takes a (“pensare a” = “to think about”), we need a cui (“about which”) rather than che (which never carries a preposition).
La volpe a cui pensavo = “the fox I was thinking about.”

Pensavo is the imperfect, which conveys an ongoing or background action in the past. Saying
“La volpe a cui pensavo ieri”
emphasizes that “I was thinking of the fox over a period yesterday,” not that the act of thinking was a single completed event. Ho pensato would sound like “I thought once.”

Yes. Stavo pensando is also the past continuous of pensare and means the same thing: “I was thinking.”
“La volpe a cui stavo pensando ieri” is perfectly acceptable and slightly more explicit about the ongoing action.

In Italian, the adjective simile is constructed with a:
essere simile a qualcosa/qualcuno = “to be similar to something/someone.”
Using di here would be incorrect.

Quella is a demonstrative pronoun meaning “that one.” It stands in for “the fox” we’re comparing:
“similar to that fox (the one) painted on the mural.”

Italian adjectives (including past participles used adjectivally) usually follow the noun or pronoun they modify when they carry descriptive meaning.
Quella dipinta = “that one painted.”
Putting dipinta before (la dipinta quella) would be ungrammatical.