Если лифт не работает, нам придётся спуститься по лестнице.

Because придётся comes from прийтись, and in the meaning to have to, this verb uses an impersonal construction.

So Russian says:

• мне придётся = I will have to
• тебе придётся = you will have to
• нам придётся = we will have to

The person who is affected goes in the dative case, not the nominative. So нам is correct, not мы.

The dictionary form is прийтись.

In this sentence, придётся means will have to or will be forced to. It is commonly followed by an infinitive:

• нам придётся спуститься = we will have to go down

This verb is a little unusual because in this meaning it is normally used impersonally.

Yes, but the nuance is different.

• нам придётся спуститься = we’ll have to go down; circumstances force it
• мы должны спуститься = we must go down; this can sound more like obligation, instruction, or duty

Here придётся is more natural because the broken elevator creates the necessity.

Because спуститься is perfective, and the sentence is talking about one complete action: going down the stairs once.

• спуститься = to go down, to descend, as a completed event
• спускаться = to be going down / to go down regularly / to go down in process

After придётся, Russian often uses the perfective infinitive when the meaning is we’ll have to do this one action.

Because the non-reflexive verb спустить usually means to lower something.

• спустить чемодан = to lower a suitcase
• спуститься = to lower oneself, meaning to go down / descend

So here -ся is part of the verb’s normal form for go down. It does not necessarily mean a literal oneself in English; it is just how Russian forms this intransitive verb.

Лестнице is dative singular.

The preposition по often takes the dative when it means movement along, on, or by way of something:

• идти по улице = to walk along the street
• подняться по лестнице = to go up the stairs
• спуститься по лестнице = to go down the stairs

So:

• лестница = staircase / stairs
• по лестнице = along / by way of the stairs

Because спуститься по лестнице is the normal way to say go down the stairs.

С лестницы usually means from the stairs / off the staircase / off the ladder, focusing on the starting point rather than the path.

So:

• спуститься по лестнице = go down the stairs
• упасть с лестницы = fall from the stairs / off a ladder

In Russian, the present tense can be used in an если clause even when the whole sentence refers to a future situation.

So Если лифт не работает can mean:

• if the elevator isn’t working
• if the elevator doesn’t work

Russian often uses the present here where English may also use present. The main clause then shows the future result:

• нам придётся... = we will have to...

Yes. That is also grammatical.

The difference is mostly one of nuance:

• Если лифт не работает sounds like if the elevator isn’t working / if it turns out not to be working
• Если лифт не будет работать sounds more explicitly future, like if the elevator will not be operating

In everyday speech, не работает is very natural.

With machines and devices, работать means to work, to function, or to be operating.

So:

• лифт работает = the elevator works / is working
• лифт не работает = the elevator doesn’t work / isn’t working / is out of order

This is the standard verb Russians use for functioning equipment.

Because Если лифт не работает is a subordinate conditional clause introduced by если.

Russian separates that clause from the main clause with a comma:

• Если лифт не работает, нам придётся спуститься по лестнице.

This is similar to English when the if clause comes first.

Yes. For example:

• Нам придётся спуститься по лестнице, если лифт не работает.

This has the same basic meaning. Russian word order is flexible, and moving parts of the sentence changes emphasis more than core meaning.

Still, putting the если clause first is very natural because it sets up the condition before the result.

The stress is on ё: при-дётся.

A helpful approximate pronunciation is pree-DYOT-sya.

Two useful things to know:

• ё is always stressed
• in fast speech, -ться / -тся often sounds close to -ца

So you may hear something like придёца, even though it is spelled придётся.