Cobras can control pests like mice and rats, it is a good idea
to have many cobras around the house for this reason.
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Yes, they do. That's one reason many people consider them to be
'pests' like crows and magpies.
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Degus are unpopular in some places, but popular in other. The
reason why they are in the US is that it is against the law to ship
them there because they are considered pests.
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Primates do, to get rid of pests that live in their hair or on
their skin. Other animals groom themselves for the same reason,
such as cats and dogs.