karakterizi

Karakterizi does two jobs, and English uses one verb for both. Somebody can characterise a thing (describe what it is like, as in the second example), and a thing can characterise something (be the feature that marks it out, as in the first and third). The second sense is the commoner one in Esperanto prose.

It is obviously a relative of karaktero, and that relation is real, but do not try to build the verb out of the noun. Esperanto's official affix list has no -iz-: the ending here is the international -ise / -ize that arrived attached to the word, not a suffix you may bolt onto roots at will. Karakterizi is learned as a whole word. The same goes for organizi, civilizi and the rest of the -iz- family, and this is exactly why they are separate dictionary entries rather than predictable builds.

Where you want plainer language, priskribi is to describe and does the first job with less ceremony. Karakterizi carries a faint air of the essay and the report, which is where you will mostly meet it.