Learn Farsi: برای شام کباب داریم.

Farsi word order is flexible, but the standard structure is Subject + Time/Context + Object + Verb. Here, the subject ما (we) is dropped, so the context phrase برای شام naturally sits at the start. It also sets the topic right away: as for dinner, we are having kebab.

Why is کباب in the singular form here, even though we might be eating multiple pieces of kebab?

In Farsi, when you are talking about a general category of food or a non-specific concept, you leave the noun in its bare, singular form. Adding a plural marker here would sound unnatural, as if you were referring to specific, distinct types of kebab rather than the meal itself.

Could I add the direct object marker را after کباب in this sentence?

No, you shouldn't use را here. The marker را is only used when the direct object is specific and definite, such as when saying 'the kebab' or 'that kebab'. Since کباب in this sentence is a general, non-specific meal, it does not take را.

Is it common to leave out the word for 'we' (ما) like this sentence does?

Yes, it is extremely common. Because the verb داریم already ends with the first-person plural suffix -یم, the listener knows exactly who is having dinner. You only need to add ما if you want to emphasize that we (and not someone else) are having kebab.