Learn Romanian: Așezați scaunele în trei rânduri!

For almost all Romanian verbs, the plural imperative (telling multiple people to do something) is exactly the same as the present tense form for voi (you plural). Since "you place" is voi așezați, the command "place!" is simply așezați!

Could I use the verb a pune (to put) instead of a așeza here?

Yes, you could say puneți scaunele! However, a așeza implies placing something carefully or arranging it in order, which is perfect for setting up chairs in specific rows.

I see that scaunele means "the chairs", but what is the base word and its gender?

The base word is scaun (chair), which is a neuter noun. Its plural is scaune. To say "the chairs", you add the plural definite article -le (used for feminine and neuter plurals) to get scaunele.

Why does the plural word for rows (rânduri) end in -uri instead of -e like scaune?

Rând is also a neuter noun, but neuter nouns do not all follow one single plural rule. While some take -e (like scaune), many others take the suffix -uri, just like timp becomes timpuri. You just have to memorize which ending each neuter noun takes!