Learn Turkish: Başkanı davet ediyoruz. - We are inviting the chairman.

Başkan means chairman or president. We add the specific direct object suffix -ı because we are inviting a specific, known chairman. If you asked the question Kimi davet ediyoruz? (Whom are we inviting?), the answer needs this same suffix: başkanı.

How would I ask "Whom are we inviting?" based on this sentence?

You just replace the object (başkanı) with the question word for "whom" (kimi). The question becomes Kimi davet ediyoruz?. Notice how both başkanı and kimi end with a vowel to show they are the specific direct object of the verb.

Why is it spelled ediyoruz? Doesn't the verb for "to do" start with et-?

Yes, the helper verb here is etmek (to do/make), which combines with davet (invitation) to mean "to invite". When we add the present continuous suffix -iyor, the hard t softens to a d so it is easier to pronounce. That is why et- plus -iyoruz becomes ediyoruz.

Where is the word for "we" in this sentence?