Learn Turkish: Arsanın çok değerli olduğunu bilseymiş, asla satmazmış. - They say if he had known that the plot of land was very valuable, he would never have sold it.

It combines the conditional -se ("if") with the inferential/reported past -miş (meaning "reportedly" or "I heard"). Instead of a standard hypothetical past like bilseydi ("if he had known"), bilseymiş means "reportedly, if he had known." It tells the listener that you heard this hypothetical scenario from someone else.

Why does the second half of the sentence use satmazmış instead of satmazdı?

To maintain the "hearsay" or reported nature established in the first clause. The structure sat-maz-dı (negative aorist + definite past) means "he wouldn't have sold it" as a definite statement. By swapping the past marker -dı for the inferential -mış, sat-maz-mış translates to "reportedly, he wouldn't have sold it."

How does the grammar in arsanın çok değerli olduğunu work to mean 'that the plot of land was very valuable'?

This is a standard noun clause acting as an object. To say "that the land was valuable", you take the genitive of the subject (arsanın, "the land's") and add the -dık participle to the verb olmak (to be). This forms olduğunu (ol + -duk + -u possessive + -n- buffer + -u accusative). It literally means "the land's being very valuable," which acts as the direct object for the verb bilmek.