Learn Polish: Ten dyrektor właśnie podpisuje umowę. - This director is signing the contract right now.

The infinitive of this verb is podpisywać (to be signing). It is formed from the perfective verb podpisać (to sign once or completely) by replacing the -ać ending with the imperfective suffix -ywać. Because it is an imperfective verb, we can use it in the present tense to describe an ongoing action.

If the infinitive is podpisywać, why does the sentence use podpisuje instead of "podpisywuje"?

Verbs created with the suffix -ywać conjugate just like verbs ending in -ować in the present tense. The -ywa- part changes to -uj- before adding the personal endings. So, for the "he/she/it" form, podpisywać becomes podpisuje.

Does właśnie always mean "right now"?

Not always; it is a very flexible word! Here, paired with an imperfective present tense verb, it emphasizes that the action is happening "right now" or "at this very moment". If paired with a past tense perfective verb, it usually means "just" (e.g., "I just signed it"). It can also mean "exactly" when agreeing with someone.

Why is the word for contract spelled umowę here instead of umowa?