Learn Turkish: İkizlerin yüzleri aynı, mizaçları ise farklı. - Twins' faces are the same, whereas their temperaments are different.

Yes, you could attach it as a suffix and write mizaçlarıysa. Both are grammatically correct. The standalone ise is often used for slightly more emphasis or in more formal writing, while the suffixed forms (-(y)sa / -(y)se) are very common in everyday speech. Both mean "whereas" or "as for" here.

Since ise is also the conditional "if", how can I tell it means "whereas" in this sentence?

Position and context give it away. When ise (or its suffix form) comes directly after a noun or pronoun to highlight a contrast with a previously mentioned subject—here, contrasting mizaçları (their temperaments) with yüzleri (their faces)—it acts as a contrastive topic marker. If it were a conditional "if", it would typically be attached to the predicate (e.g., if it is different).

Does the genitive word ikizlerin apply to both halves of the sentence?

Exactly. İkizlerin (of the twins) serves as the owner for both possessed nouns in the sentence. It modifies both yüzleri (their faces) and mizaçları (their temperaments). Because the connection is obvious, you don't need to repeat ikizlerin or add onların before the second noun.

Why doesn't the ç in mizaçları mutate to c?