Learn Swedish: Förståelsen ökade medan fattigdomen minskade. - The understanding increased while the poverty decreased.

The word förståelse (understanding) is built from the verb förstå (to understand) plus the suffix -else. This suffix turns verbs into abstract nouns. Because words ending in -else are typically en-words, the definite form simply adds an -n to the end, giving us förståelsen (the understanding).

What type of words take the -dom suffix, like in fattigdomen?

The suffix -dom is used to create abstract nouns describing a state, condition, or domain. It is usually attached to adjectives—like turning fattig (poor) into fattigdom (poverty)—or to nouns, like barn (child) into barndom (childhood). Almost all -dom words are en-words, which is why it becomes fattigdomen in the definite form.

Do öka and minska need to be in the passive voice here since things are "being increased" or "decreased"?

No. Just like "increase" and "decrease" in English, öka and minska can be used both transitively (when someone actively increases or decreases something) and intransitively (when a value or amount changes on its own). Here, they are intransitive, so you just use the active past tense forms ökade and minskade.

Medan is a subordinating conjunction. Why doesn't the word order in medan fattigdomen minskade look like a subordinate clause?