Learn Hardcore Italian: La volpe a cui pensavo ieri è proprio simile a quella dipinta nel murale. - The fox I was thinking of yesterday is really similar to the one painted in the mural.

“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.”

Why is pensavo in the imperfect tense instead of a simple past like ho pensato?

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.”

Can we drop the preposition a and say la volpe cui pensavo ieri?

No. In Italian you can’t omit the preposition required by the verb. Because pensare requires a, you must say a cui. Dropping it would be ungrammatical.

Could we rephrase a cui pensavo as a cui stavo pensando?

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.

What does proprio add in è proprio simile?

Here, proprio is an intensifier meaning “really” or “exactly.” It emphasizes the closeness of the resemblance: “is really/so similar.”

Why do we say simile a and not simile di?

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.

What does quella refer to in simile a quella dipinta?

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.”

Why is dipinta (the past participle) placed after quella? Could it come before?

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.

What does murale mean, and why not muro?

Murale refers to the mural painting itself (the artwork on a wall). Muro is simply a wall. So dipinta nel murale means “painted in/on the mural,” whereas sul muro would just mean “on the wall” without implying a work of art.

What is the plural of murale: murali or murales?

Both forms appear, but the standard Italian plural is murales (invariant, following its French origin). Murali also exists but is less common.