Learn Spanish (Latin America): Esperamos en el túnel por tres minutos.

Esperar means "to wait for" when you are talking about what or who you are waiting for (like Esperamos el tren for "We wait for the train"). However, the por in this sentence belongs to the time phrase (por tres minutos). Here, por is used strictly to express the duration of the wait.

Could we use para instead of por to say "for three minutes"?

No. Whenever you are talking about the duration of an action (how long it lasts) you must use por. Para is used for deadlines or destinations, but never for a length of time.

How do I know if esperamos means "we wait" (present) or "we waited" (past)?

You have to rely on context! For regular -ar verbs like esperar, the "we" form is exactly the same in both the present tense and the preterite (completed past) tense. Without extra context, this sentence could just as easily mean "We waited in the tunnel for three minutes."

Is it possible to drop the word por entirely in this sentence?

Yes! Just like in English where we sometimes say "We wait three minutes" instead of "We wait for three minutes," Spanish speakers frequently drop por when talking about duration. Saying Esperamos en el túnel tres minutos is completely correct and very common in everyday speech.