Kız kardeşim utandı, ben ise gülmeye devam ettim.

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Breakdown of Kız kardeşim utandı, ben ise gülmeye devam ettim.

• benim: my
• kız kardeş: the sister
• devam etmek: to continue

Questions & Answers about Kız kardeşim utandı, ben ise gülmeye devam ettim.

What does the particle bolded as ise do here, and how is it different from ama or de/da?

ise marks a contrastive topic: “as for … / whereas …”. It contrasts the second clause with the first: “My sister got embarrassed; as for me, I kept laughing.”

• ama is a coordinating conjunction meaning “but” and links clauses: “Kız kardeşim utandı, ama ben gülmeye devam ettim.”
• de/da means “also/too,” not contrast. “Ben de gülmeye devam ettim” = “I also kept laughing,” which would imply your reaction was the same, not opposite.

Can I write bense instead of ben ise?

Yes. bense is the fused/clitic form and is very common, especially in writing. All of these are natural:

• “Kız kardeşim utandı; ben ise gülmeye devam ettim.”
• “Kız kardeşim utandı; bense gülmeye devam ettim.”

Why is there a comma, and could I use a semicolon?

You have two independent clauses. A comma is common in everyday writing; a semicolon is also good (and slightly more formal/clear):
“Kız kardeşim utandı; ben ise gülmeye devam ettim.”

Why is the pronoun ben expressed? Isn’t the subject on the verb already?

Turkish usually drops subject pronouns, but they are used for emphasis/contrast. ise needs a topic to attach to, so ben (or the fused bense) is expressed to mark “as for me.” Without contrast, you could just say “Gülmeye devam ettim.”