Hat die Polizei irgendwelche Verdächtige?

English Translation

Do the police have any suspects?

Amongst the many German words that mean “any”, why was the choice here “irgenwelche”? Are there any bona fide alternatives iin this contexr?

In this context, not really. For plural you normally express “any” by omitting the article or determiner.
So you could say:
Hat die Polizei Verdächtige?
But this sounds a little too general, and the idiomatic way is to add “schon”:
Hat die Polizei schon Verdächtige?

In negative sentences you would normally use “kein”:
Die Polizei hat noch keine Verdächtigen. - The police don’t have any suspects yet. (= has no suspects)

Amongst the many German words that mean “any”

Which ones do you mean? German does not really have an equivalent for “any”, and usually expresses things in different ways. (I listed some examples here: Er kommt jeden Moment.). And “irgendwelche” really is a kludge, because it means a little more than just “any”. It’s closer to “any kind of”.

Also note that the german sentence is wrong, and it should be “irgendwelche Verdächtigen”, because “Irgendwelche” is a determiner that causes weak declension.
See the declension table at Verdächtiger - Wiktionary, the free dictionary

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