Learn Spanish (Spain): Los niños parecen estar cansados.

Yes, absolutely. Los niños parecen cansados translates to "The children look tired" or "The children seem tired." Adding estar makes it specifically "seem to be tired," which is a slight stylistic choice but means essentially the same thing in everyday conversation.

Why is cansados plural if it comes immediately after the infinitive estar?

Even though cansados follows the infinitive estar, it acts as an adjective describing the main subject of the sentence, los niños. In Spanish, adjectives must always agree in gender and number with the noun they describe, regardless of how many verbs separate them.

What would it mean if we used ser instead of estar here, as in parecen ser cansados?

It would completely change the meaning! With estar, cansado means "tired" (a temporary physical state). With ser, cansado means "tiring" or "annoying" (an inherent characteristic). So parecen ser cansados would mean "The children seem to be tiring" or "The children seem to be annoying."

Why isn't this sentence using the reflexive verb parecerse?