Ветрозащитная куртка и гамаши уже готовы.

In Russian, the verb to be is usually omitted in the present tense.

So:

• Ветрозащитная куртка и гамаши уже готовы.
• literally: Windproof jacket and gaiters already ready.

English needs are, but Russian normally does not:

• Я дома. = I am at home.
• Она врач. = She is a doctor.

If the sentence were in the past or future, Russian would use a form of быть:

• ... были готовы = ... were ready
• ... будут готовы = ... will be ready

Because the subject is two things together:

• ветрозащитная куртка
• гамаши

They are joined by и (and), so the whole subject is plural. That means the predicate must also be plural:

• куртка ... готова = the jacket is ready
• гамаши ... готовы = the gaiters are ready
• куртка и гамаши ... готовы = the jacket and the gaiters are ready

So готовы agrees with the whole compound subject.

This is a very common question. Russian often uses the short form of adjectives after the subject when they mean a state or condition.

Here, готовы is the short form of готовые.

Compare:

• готовые вещи = ready things
  
  • full adjective form, used before a noun
• вещи готовы = the things are ready
  
  • short adjective form, used as the predicate

So in this sentence:

• куртка и гамаши уже готовы = the jacket and gaiters are already ready

Using готовые here would generally sound wrong in standard Russian, because after the subject Russian normally wants the short form for this meaning.

Because it describes куртка, and куртка is a feminine singular noun.

Russian adjectives must agree with the noun they modify in:

• gender
• number
• case

So:

• ветрозащитная куртка = feminine singular
• ветрозащитный костюм = masculine singular
• ветрозащитное пальто = neuter singular
• ветрозащитные вещи = plural

In this sentence, the adjective belongs only to куртка, so it takes the feminine singular form ветрозащитная.

Гамаши is normally used as a plural-only noun in modern Russian, much like some clothing words in English:

• pants
• scissors
• glasses

So Russian treats гамаши as a plural item:

• эти гамаши = these gaiters
• новые гамаши = new gaiters
• гамаши готовы = the gaiters are ready

A singular form is not normally used in everyday speech for the usual meaning.

The main nouns are in the nominative case, because they are the subject of the sentence.

• ветрозащитная куртка = nominative singular
• гамаши = nominative plural

You can tell because the sentence is saying what these things are like / what state they are in:

• The windproof jacket and gaiters are already ready.

The adjective ветрозащитная also matches nominative singular feminine because it modifies куртка.

And готовы is a short-form predicate adjective agreeing in number with the whole subject.

In this sentence, it most naturally describes only куртка.

So the structure is:

• [ветрозащитная куртка] и [гамаши] уже готовы

That means:

• the windproof jacket and the gaiters are already ready

If the speaker wanted to make it clear that both items are windproof, Russian would usually say something like:

• ветрозащитная куртка и ветрозащитные гамаши
• or rephrase the sentence in another clearer way

So as written, a learner should understand ветрозащитная as modifying куртка only.

Уже usually means already, and in this sentence it modifies the idea of being ready:

• already ready

Russian word order is flexible, but this placement is very natural:

• Ветрозащитная куртка и гамаши уже готовы.

It could be moved for emphasis, for example:

• Уже готовы ветрозащитная куртка и гамаши.
• Ветрозащитная куртка и гамаши готовы уже.
  This is much less neutral and sounds marked.

So the sentence uses the most normal, neutral order.

Yes. It is a compound adjective made from the ideas of:

• ветер = wind
• защита / защитный = protection / protective

So ветрозащитный means something like:

• wind-protective
• wind-resistant
• windproof

In natural English, windproof jacket or wind-resistant jacket is usually the best translation, but grammatically the Russian word is a single adjective.

No. Once you have куртка и гамаши together as the subject, Russian normally treats that as plural, so the predicate must be plural too:

• Куртка и гамаши уже готовы.

Using готова would only agree with куртка, and that would be incorrect here.

Compare:

• Куртка уже готова. = The jacket is ready.
• Гамаши уже готовы. = The gaiters are ready.
• Куртка и гамаши уже готовы. = The jacket and the gaiters are ready.

Yes. Готов and its forms often mean ready, but depending on context they can also suggest:

• prepared
• finished
• done
• available for use

In this sentence, уже готовы most naturally means that the items are now prepared / finished / ready to use.

So the exact English wording depends on context:

• are already ready
• are already prepared
• are already done

But grammatically, it is the standard adjective готов in the plural short form готовы.