All of the sentences you provided contain both noun phrases and verb phrases. However, to clarify:
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"You can find frogs and insects by the pond if you look closely enough."
- Noun Phrase: "frogs and insects"
- Verb Phrase: "can find"
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"Some dog breeds have docked tails."
- Noun Phrase: "Some dog breeds"
- Verb Phrase: "have docked tails"
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"He sat on my grandmother’s favorite armchair."
- Noun Phrase: "my grandmother’s favorite armchair"
- Verb Phrase: "sat"
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"The pigeons have not landed on my neighbor’s balcony in a long time."
- Noun Phrase: "The pigeons" and "my neighbor’s balcony"
- Verb Phrase: "have not landed"
So, to answer your question directly, all four sentences contain both a noun phrase and a verb phrase.