Я никогда не открывал кокос дома без помощи брата.

Russian normally uses negative concord, which means multiple negative words appear together in the same sentence.

So:

• никогда = never
• не открывал = did not open / have not opened

Together, Я никогда не открывал... is the normal Russian way to say I have never opened...

You usually should not drop не here.
So Я никогда открывал... would be incorrect.

This is a question of aspect.

• открывал = imperfective
• открыл = perfective

With никогда, Russian often uses the imperfective to talk about something that has never happened in one’s experience.

So Я никогда не открывал кокос... means something like:

• I have never opened a coconut...
• I never used to open a coconut... depending on context

If you used открыл, it would sound more like referring to a specific completed event, which does not fit as naturally with this general never in my life / never at all meaning.

That is the normal marker of the past tense in Russian.

In the past tense, the verb also shows gender in the singular:

• открывал = masculine speaker
• открывала = feminine speaker
• открывало = neuter
• открывали = plural

So this sentence suggests the speaker is male.
If a woman said it, it would be:

Я никогда не открывала кокос дома без помощи брата.

Because кокос is the direct object, so it goes in the accusative case. But for inanimate masculine nouns, the accusative singular is the same as the nominative singular.

So:

• nominative: кокос
• accusative: кокос

That is why the form does not change.

Compare with an animate masculine noun:

• Я вижу брата = I see my/the brother Here the accusative looks like the genitive because брат is animate.

Here дома means at home.

This is a very common Russian adverbial use:

• Я дома = I am at home
• работать дома = to work at home
• есть дома = to eat at home

By contrast, в доме means more literally in the house/building.

So:

• дома focuses on the idea of being at home
• в доме focuses more on being inside the house

In this sentence, дома is the natural choice for at home.

The preposition без always requires the genitive case.

So:

• помощь = nominative
• без помощи = without help

That is why помощь changes to помощи.

This is a very useful pattern to remember:

• без сахара = without sugar
• без воды = without water
• без помощи = without help

Here брата means of (my/the) brother.

The phrase помощь брата literally means:

• the brother’s help
• help of (my/the) brother

So брата is in the genitive singular.

The full structure is:

• без
  • genitive → без помощи
• помощь кого? → брата

So без помощи брата = without my brother’s help

Russian often leaves out possessive words like my, your, his, etc. when the meaning is already clear from context.

So брата here can naturally be understood as:

• my brother
• sometimes the brother, depending on context

If you want to make it explicit, you can say:

Я никогда не открывал кокос дома без помощи моего брата.

That is correct too, but the shorter version sounds perfectly natural.

No, Russian word order is fairly flexible. The sentence given is a natural, neutral version:

Я никогда не открывал кокос дома без помощи брата.

But you could move parts around for emphasis, for example:

• Я дома никогда не открывал кокос без помощи брата.
• Кокос я никогда не открывал дома без помощи брата.

The basic meaning stays the same, but the emphasis changes.

A useful point:

• никогда usually appears near the verb it relates to
• the original order sounds straightforward and natural

Yes, the imperfective form открывал can suggest a general past experience or something that never happened as a repeated action.

So depending on context, it may be understood as:

• I have never opened a coconut at home without my brother’s help or
• I never used to open a coconut at home without my brother’s help

In many situations, English would naturally translate it with have never opened, but the Russian imperfective leaves some room for that broader, habitual sense.