Если завтра снова будет дождь, я возьму дождевик и кепку.

That is a very common difference between English and Russian.

In Russian, after если (if), you can use the future tense when you are talking about a real future possibility:

• Если завтра будет дождь, ... = If it rains / if there is rain tomorrow, ...
• Я возьму... = I’ll take...

So Russian does not follow the same rule as English here. English usually uses the present tense after if for future meaning, but Russian normally uses the actual future tense.

So this sentence is completely natural:

• Если завтра снова будет дождь, я возьму дождевик и кепку.

Both are possible, but they are a little different in feel.

• будет дождь literally means there will be rain
• будет идти дождь literally means rain will be going / falling

In everyday Russian, будет дождь is very common and natural when talking about the weather forecast or the general condition:

• Завтра будет дождь. = It will rain tomorrow.

If you say будет идти дождь, it sounds a bit more explicit about the process of rain falling:

• Завтра весь день будет идти дождь. = It will be raining all day tomorrow.

So in your sentence, будет дождь is shorter and very idiomatic.

Because in будет дождь, the noun дождь is the subject of the expression.

Russian often expresses weather with structures like:

• Будет дождь. = There will be rain.
• Был снег. = There was snow.
• Будет ветер. = There will be wind.

In these patterns, the weather noun is in the nominative case because grammatically it acts like the thing that is / will be.

So:

• дождь = nominative singular

Because взять / возьму is perfective, and here Russian wants a single completed action: I’ll take / I’ll bring along.

Compare:

• я возьму дождевик = I’ll take a raincoat
  one definite action

• я буду брать дождевик = I will be taking a raincoat
  this sounds unusual here, because it focuses on the process rather than the result

Russian often uses the simple future of a perfective verb for one-time future actions:

• сделаю = I’ll do
• куплю = I’ll buy
• возьму = I’ll take

So я возьму дождевик и кепку is exactly what you would expect.

Because both nouns are direct objects, so they go into the accusative case, but their accusative forms look different.

• дождевик is masculine inanimate
  accusative singular = same as nominative singular
  so: дождевик → дождевик

• кепка is feminine
  accusative singular usually changes -а to -у
  so: кепка → кепку

That is why the sentence says:

• возьму дождевик и кепку

This is a very important Russian pattern:

• masculine inanimate: often no visible change in accusative
• feminine in -а: usually -а → -у
• feminine in -я: usually -я → -ю

Because Если завтра снова будет дождь is a subordinate clause introduced by если.

Russian separates this kind of conditional clause with a comma:

• Если будет дождь, я останусь дома.
• Если у меня будет время, я позвоню.

So in your sentence:

• Если завтра снова будет дождь, я возьму дождевик и кепку.

The comma marks the boundary between:

1. the condition: If it rains again tomorrow
2. the main result: I’ll take a raincoat and a cap

Снова means again.

In this sentence:

• Если завтра снова будет дождь... = If it rains again tomorrow...

It tells us that rain has already happened recently, and the speaker thinks it may happen another time.

Its position is fairly flexible, though word order can slightly change emphasis:

• Если завтра снова будет дождь...
  neutral, natural

• Если снова завтра будет дождь...
  less natural in most contexts

• Если завтра будет снова дождь...
  possible, but less standard

The version in your sentence is the most natural one.

Usually yes, in most learner contexts дождевик is best translated as raincoat.

More literally, дождевик is something worn for rain, often a lightweight waterproof outer layer. Depending on context, it could mean:

• a raincoat
• a waterproof poncho
• some other simple rain cover

So дождевик is a good practical word for rainy weather clothing.

Because Russian, like English, usually uses one and to connect the last item in a short list.

So:

• дождевик и кепку = a raincoat and a cap

You could repeat и in some contexts for emphasis:

• и дождевик, и кепку

But that would mean something more like:

• both the raincoat and the cap
• the raincoat as well as the cap

In your sentence, the simple version is the normal one.

Not if you mean I’ll take a raincoat and a cap as two separate items.

• дождевик и кепку = a raincoat and a cap
• дождевик с кепкой = a raincoat with a cap

The second version sounds like the raincoat somehow comes together with a cap, as one combined set, or that the cap is attached/associated with it. That is not the intended meaning here.

So for two separate things, и is correct.

Yes, Russian word order is flexible, but the original sentence is the most neutral and natural.

Original:

• Если завтра снова будет дождь, я возьму дождевик и кепку.

Possible variations:

• Я возьму дождевик и кепку, если завтра снова будет дождь.
• Если завтра будет дождь снова, я возьму дождевик и кепку.
  grammatical, but less natural

Why keep the original order?

• the if clause comes first
• the condition is presented before the result
• it sounds smooth and standard

So although other versions are possible, your sentence is a very good default model.

Because Russian often does not use a dummy subject like English it.

English says:

• It will rain
• It is cold
• It is getting dark

Russian often says these without an equivalent of English it:

• Будет дождь.
• Холодно.
• Темнеет.

So Russian simply expresses the event or condition directly, without inserting a meaningless subject pronoun.

That is why Если завтра снова будет дождь... is complete all by itself.