Learn Spanish (Latin America): Durante la charla, preguntó si teníamos compatibilidad. - During the chat, he asked if we had compatibility.

This sentence uses past reported speech. If the person originally asked the direct question in the present tense (¿Tenemos compatibilidad?), we have to shift the tense backwards when reporting it later. Since the reporting verb (preguntó) is in the past, the present tense tenemos shifts back to the imperfect teníamos.

Why doesn't si have an accent mark if it's reporting a question?

In Spanish, standard question words like qué and dónde keep their accent marks even in indirect questions. However, si here means "if" or "whether", not "yes" (sí). The word for "if" never takes an accent mark, even when it is used to introduce an indirect yes/no question.

Why use the preterite preguntó rather than the imperfect preguntaba?

We use the preterite preguntó because the act of asking this specific question was a single, completed event during the conversation. If we used preguntaba, it would imply he was repeatedly asking it, or was in the middle of asking it when something else happened.

What kind of "chat" does charla refer to?

charla is a versatile word. It can mean a casual conversation or chat between two people, but it is also commonly used for a formal talk, lecture, or presentation. Given the context of discussing compatibility, this was likely a one-on-one conversation, perhaps a date or an interview.