Here are the combined sentences using the specified punctuation:
Semicolon: New Sentence: The cat spotted the penguins; they were waddling around, just as he had imagined.
Colon for clarification: New Sentence: There was one thing the cat couldn’t wait to do: he couldn’t wait to see the penguins dive into the water.
Colon to introduce a list: New Sentence: The cat noticed several things in the penguin exhibit: rocks, icy pools, and playful penguins sliding around.
Colon to introduce a quote: New Sentence: The cat watched the penguins and thought of something his mother always said: "Adventure is out there, waiting for you."