Ef handriðið væri sterkara, myndi hún ganga hraðar niður stigann.

Because this sentence describes a hypothetical, unreal situation: if the handrail were stronger, she would walk down the stairs faster.

• væri is the subjunctive past form of vera (to be)
• myndi is the conditional form used for would

This is the normal Icelandic way to express a counterfactual or unlikely condition.

Compare:

• Ef handriðið er sterkara, gengur hún hraðar niður stigann.
  = If the handrail is stronger, she walks / will walk down the stairs faster.
  This sounds more like a real possibility.

• Ef handriðið væri sterkara, myndi hún ganga hraðar niður stigann.
  = If the handrail were stronger, she would walk down the stairs faster.
  This is hypothetical.

Væri is a form of vera (to be). Specifically, it is the past subjunctive.

In Icelandic, the past subjunctive is often used for present-time unreal conditions, just like English were in formal English:

• Ef ég væri ríkur... = If I were rich...
• Ef handriðið væri sterkara... = If the handrail were stronger...

So even though it looks like a past form, it does not necessarily mean past time here. It signals unreality or hypothetical meaning.

Myndi is the conditional form of munu, and in sentences like this it usually translates as would.

Here:

• myndi hún ganga = she would walk

It agrees with the subject hún in number, so it is singular.

This pattern is very common in Icelandic counterfactual sentences:

• Ef ég hefði tíma, myndi ég koma.
  = If I had time, I would come.

This is because Icelandic is a verb-second language in main clauses.

The sentence begins with the if-clause:

• Ef handriðið væri sterkara

After that, the main clause starts, and the finite verb comes first:

• myndi hún ganga...

So the structure is:

• fronted clause
• finite verb
• subject
• rest of the sentence

If you put the main clause first, you get:

• Hún myndi ganga hraðar niður stigann ef handriðið væri sterkara.

That is also correct.

Because handriðið is the definite singular form of handrið.

• handrið = a handrail / handrail
• handriðið = the handrail

Icelandic usually adds the definite article as a suffix to the noun, instead of using a separate word like English the.

So:

• handrið = indefinite
• handriðið = definite

Also, handrið is a neuter noun, which is why the definite ending is -ið here.

Sterkara is the comparative form of sterkur (strong) and it matches the noun handriðið, which is neuter singular.

Here the adjective is used predicatively after vera:

• handriðið væri sterkara
  = the handrail were stronger

The important points are:

• base adjective: sterkur = strong
• comparative: sterkari / sterkara = stronger
• because handriðið is neuter singular, the form here is sterkara

Compare:

• maðurinn væri sterkari = the man were stronger
• konan væri sterkari = the woman were stronger
• barnið væri sterkara = the child were stronger

Because Icelandic, like English, can use a comparative without explicitly stating what it is compared to.

So:

• sterkara = stronger

The comparison is understood from context: stronger than it is now, or stronger than it actually is.

If you want, you can make it explicit:

• Ef handriðið væri sterkara en það er núna...
  = If the handrail were stronger than it is now...

But in many sentences, leaving out en... is completely natural.

Because hraðar is an adverb, while hraðari is an adjective.

Here it modifies the verb ganga:

• ganga hraðar = walk faster

So you need the adverb.

Compare:

• hún gengur hraðar = she walks faster
• hún er hraðari = she is faster

A useful contrast:

• hraður / hröð / hratt = fast
• adjective comparative: hraðari = faster
• adverb comparative: hraðar = faster

Because stigann is the accusative singular definite form of stigi (stairs, staircase in this context), and after expressions of movement in a direction, Icelandic often uses the accusative.

So:

• niður stigann = down the stairs / down the staircase

This is directional: she is moving downward along the stairs.

Useful forms:

• stigi = staircase / stairs
• stiginn = the staircase (nominative)
• stigann = the staircase (accusative)
• stiganum = the staircase (dative)

Here the motion is toward/down along the stairs, so stigann is expected.

Ganga niður stigann means walk down the stairs.

Yes, Icelandic could use other verbs depending on nuance. For example:

• ganga = walk
• fara = go
• labba = walk, often more casual

So:

• hún myndi ganga hraðar niður stigann
  suggests actual walking movement

• hún myndi fara hraðar niður stigann
  is also possible, but fara is more general

In this sentence, ganga is a natural choice because the action is specifically walking down stairs.

It talks about a present or future hypothetical situation, not a past one.

Even though væri looks like a past form, in Icelandic it is commonly used in unreal present-time conditions.

So this sentence means something like:

• right now, the handrail is not stronger
• in that hypothetical situation, she would go down the stairs faster

If you wanted a past counterfactual, Icelandic would normally use a different structure, for example:

• Ef handriðið hefði verið sterkara, hefði hún gengið hraðar niður stigann.
  = If the handrail had been stronger, she would have walked down the stairs faster.

So:

• væri / myndi ganga → unreal present/future
• hefði verið / hefði gengið → unreal past

Not always. It depends on whether the condition is real/open or hypothetical/unreal.

With a real or possible condition, Icelandic can use normal indicative forms:

• Ef handriðið er sterkt, gengur hún niður stigann.
  = If the handrail is strong, she walks down the stairs.

With a hypothetical or contrary-to-fact condition, Icelandic often uses the subjunctive/conditional pattern:

• Ef handriðið væri sterkara, myndi hún ganga hraðar niður stigann.

So ef itself does not automatically force one form; the meaning of the sentence determines the grammar.