Learn Finnish: Sekä joukko että poliisi etsivät uhria kaikin voimin. - Both the group and the police searched for the victim with all their might.

The instructive case adds -in to the plural stem of a word to describe how an action is done. Here, both kaikki (stem kaikk-) and voima (plural stem voim-) take the ending to make kaikin voimin (with all might). This case is mostly used in fixed idiomatic expressions like this one, rather than being freely attached to any everyday noun.

Could I use the adessive case (kaikilla voimilla) instead of the instructive here?

Grammatically, the adessive (-lla/-llä) is the standard way to say you do something with a tool or instrument. However, kaikin voimin is a deeply established idiom in Finnish. Using the adessive here would sound clunky and unnatural to a native speaker, even though the literal meaning is identical.

Joukko and poliisi are singular nouns. Why is the verb etsivät plural?

When two subjects are connected by the conjunction pair sekä ... että (both ... and), they combine to form a plural subject. Because multiple parties are doing the action, the verb must take the plural -vat ending.

Is the verb etsivät in the present or past tense here?