Learn Hardcore Spanish (Spain): Tenemos que correr para no perder el tren. - We have to run so we don’t miss the train.

It expresses obligation or necessity, similar to “have to” in English. So tenemos que correr = “we have to run.” After que, you must use an infinitive (here, correr), not a conjugated verb.

Why is que used after tenemos? Is it the same as “that”?

In this construction, que is an unstressed particle that links tener to an infinitive: tener que + infinitive. It doesn’t translate as “that.” Think of it as a fixed pattern meaning “to have to do [something].”

Could I use deber or haber de instead of tener que?

Deber + infinitive suggests duty/advisability and can sound a bit more formal or moral: Debemos correr… (“We ought to/must run…”).
Haber de + infinitive (e.g., Hemos de correr…) is a bit formal/literary in Spain, and often weaker than “have to.”
Tener que is the most common, everyday way to say “have to.”

Why is it para no + infinitive? What does that part do?

Para + infinitive expresses purpose (“in order to”). With no, it becomes a negative purpose (“in order not to”). So para no perder el tren = “so as not to miss the train.”