Nos quedamos en casa hasta que pase la tormenta.

In this meaning (to stay / to remain), Spanish normally uses the pronominal (reflexive-looking) verb quedarse: quedarse en casa = to stay at home.
Quedar without se often means things like to be located (La farmacia queda cerca) or to agree/arrange (Quedamos mañana = We’ll meet tomorrow).

Nos is the pronoun that matches quedarse for we. It indicates that the subject (we) is also the “recipient” of the staying. In natural English we don’t say “we stayed ourselves,” but Spanish uses this structure:

• Yo me quedo = I stay
• Tú te quedas = You stay
• Nosotros nos quedamos = We stay

It’s preterite (simple past): Nos quedamos = We stayed / We ended up staying.
If you want We’re staying / We stay, you’d use present: Nos quedamos en casa hasta que pase la tormenta can also appear with present as a habit/plan depending on context, but nos quedamos by itself is formally the preterite form.

Spanish often uses the present (or sometimes a form that looks identical to another tense) to talk about near-future plans in context, but in this exact form, nos quedamos is most straightforwardly preterite.
For an unambiguous future idea, common options are:

• Nos vamos a quedar en casa hasta que pase la tormenta. (going to stay)
• Nos quedaremos en casa hasta que pase la tormenta. (will stay)

Because hasta que often triggers the subjunctive when the action after it is not completed yet / is uncertain / is in the future from the speaker’s viewpoint.

• hasta que pase la tormenta = until the storm passes (hasn’t happened yet) → subjunctive: pase
  You use indicative (pasa) when you’re talking about something habitual or factual:
• Siempre esperamos hasta que pasa la tormenta. = We always wait until the storm passes. (a repeated, “known” pattern)

Pase is present subjunctive of pasar. With la tormenta as the subject, pasar means to pass / to go by / to be over: que pase la tormenta = for the storm to pass / until the storm passes.

Yes, both are correct:

• hasta que pase la tormenta
• hasta que la tormenta pase
  The first is very common and sounds natural; the second can feel a bit more explicit/emphatic because you name the subject (la tormenta) before the verb.

Because en expresses location/state: staying at home = quedarse en casa.
A is for movement/destination: go home = ir a casa / venir a casa.
So:

• Nos quedamos en casa = We stay at home
• Nos vamos a casa = We go home

La is the definite article the. In Spanish you typically include the article with a specific event like this: la tormenta = the storm. It sounds more natural than omitting it.

Yes: la tormenta, feminine. You can tell from common dictionary entries and from the article/adjective agreement:

• una tormenta fuerte (feminine adjective form: fuerte doesn’t change here, but others would: una tormenta intensa)

Often it simply means to stay with no drama. But quedarse can sometimes suggest ending up staying or remaining (instead of leaving) depending on context. If you want to stress “stuck,” Spanish might add something like tener que (have to) or a clarifier:

• Nos tenemos que quedar en casa… = We have to stay at home…
• Nos quedamos en casa porque no se puede salir. = We stayed home because you can’t go out.

Yes:

• Nos quedaremos en casa… = more formal/neutral “will stay”
• Nos vamos a quedar en casa… = very common in Latin America for “going to stay” (planned/near future)
• Nos quedamos en casa… = can be past (“we stayed”) or present-in-context (“we’re staying”), but by form it’s the preterite and needs context to be future-like.