Я никогда не готовила чизкейк дома, но хочу попробовать.

In the past tense, Russian verbs agree with the subject in gender and number.

• готовил = a man was cooking / prepared
• готовила = a woman was cooking / prepared
• готовили = they were cooking / prepared

So Я никогда не готовила... would be said by a female speaker. A male speaker would say Я никогда не готовил чизкейк дома, но хочу попробовать.

Yes, it is a double negative, and that is normal and required in standard Russian.

Russian usually uses negative words together with не:

• Я никогда не готовила = I have never cooked/prepared
• Я ничего не знаю = I know nothing
• Я никого не вижу = I see nobody

In English, using two negatives is usually nonstandard, but in Russian it is the correct pattern.

Готовить / приготовить often means to cook, to prepare, or more generally to make food.

So in this sentence, готовила чизкейк means something like:

• made cheesecake
• prepared cheesecake
• sometimes loosely cooked cheesecake

For cheesecake specifically, Russians may also say печь / испечь because cheesecake is baked:

• Я никогда не пекла чизкейк дома = I’ve never baked cheesecake at home

Both are possible, but готовить is a broad, very common verb for making food.

Here чизкейк is a direct object, so it is in the accusative case.

But чизкейк is:

• masculine
• inanimate
• singular

For masculine inanimate nouns, the accusative singular is usually the same as the nominative singular.

So:

• nominative: чизкейк
• accusative: чизкейк

That is why the word does not change here.

Дома is a very common adverb meaning at home.

So:

• Я дома = I am at home
• готовить дома = to cook at home

You do not need a preposition like в here.

Compare:

• дома = at home
• в доме = in the house/building

So чизкейк дома means cheesecake at home / homemade cheesecake depending on context, and here it naturally means at home.

Russian often omits the subject pronoun when it is clear from the verb form or context.

The full version would be:

• Я никогда не готовила чизкейк дома, но я хочу попробовать.

But repeating я is unnecessary here. Russian commonly says:

• Я никогда не готовила..., но хочу попробовать.

This sounds natural and avoids repetition.

This is about aspect.

• пробовать = imperfective
• попробовать = perfective

After хочу, Russian often uses the perfective infinitive when talking about doing something once, having a go, or trying it out.

So:

• хочу попробовать = I want to try it / give it a try

If you said хочу пробовать, it would sound more like wanting to be trying, try repeatedly, or focus on the process, which is less natural here.

In Russian, the object can be omitted if it is obvious from context.

Here, попробовать means:

• try making it
• try making cheesecake
• try doing that

Because the first part already mentions готовить чизкейк дома, Russian does not need to repeat it.

A fuller version could be:

• ...но хочу попробовать приготовить его дома.
• ...но хочу попробовать испечь чизкейк дома.

But the shorter version is very natural.

In this sentence, it most naturally means I have never made/cooked...

Russian does not have a separate tense exactly like the English present perfect. It often uses the past tense plus words like никогда to express that idea.

So:

• Я никогда не готовила чизкейк дома = I have never made cheesecake at home

Even though the verb form is past tense, the meaning can match English have never done.

This is a very normal Russian word order:

• Я = subject
• никогда = never
• не готовила = did not make / have never made
• чизкейк = object
• дома = at home
• но хочу попробовать = but want to try

Russian word order is fairly flexible, but this order is neutral and natural.

You could move some parts for emphasis, for example:

• Я чизкейк дома никогда не готовила...
  This puts more emphasis on cheesecake at home.

But the original sentence is the most straightforward.

It is a borrowed word from English, but it is commonly used in Russian.

Russian has many loanwords for foods and modern items. Чизкейк behaves like a regular masculine noun in many contexts:

• чизкейк
• чизкейка
• чизкейку, etc.

So even though it comes from English, it fits naturally into Russian grammar.

Yes, that is possible.

Compare:

• готовила чизкейк = cooked/prepared/made cheesecake
• делала чизкейк = made cheesecake

Делать is more general, while готовить sounds more specifically connected to food preparation. In this context, готовила is a very natural choice.

The main stresses are:

• Я никогдá не готóвила чизкéйк дóма, но хочý попробóвать.

A few helpful notes:

• никогдá → stress on the last а
• готóвила → stress on то
• чизкéйк → stress on кей
• дóма → stress on the first syllable
• хочý → stress on the last syllable
• попробóвать → stress on бо

Stress is important in Russian, so it is worth learning these early.