Если дома есть майонез, уксус и немного зелени, салат получается вкуснее.

Yes, дома literally means at home, but in sentences like this it often means in the house / at home / available at home.

So Если дома есть майонез... means something like:

• If there is mayonnaise at home
• If you have mayonnaise at home

Russian often uses есть + a place instead of saying you have directly.

Both are possible, but they mean slightly different things.

• Если дома есть майонез... = If there is mayonnaise at home / if mayonnaise is available at home
• Если у нас есть майонез... = If we have mayonnaise

The version with дома sounds more general and natural in everyday speech when talking about ingredients available in the house.

No. Here есть means there is / there are.

Russian есть can mean two different things:

• есть = to eat
• есть = there is / there are / exists

In this sentence, it is clearly the second meaning:

• дома есть майонез = there is mayonnaise at home

These words are the things that exist / are available, so they are in the form normally used for the subject-like part of the sentence.

• майонез — nominative singular
• уксус — nominative singular
• немного зелени — a quantity expression

The first two appear in their basic dictionary forms.
The third one is different because немного affects the case of the noun after it.

Because after words of quantity like много, мало, немного, сколько, Russian usually uses the genitive case.

So:

• немного зелени = a little greenery / a few herbs / some greens

Here:

• зелень is the dictionary form
• зелени is the genitive singular form

This is a very common pattern:

• много воды = a lot of water
• немного сахара = a little sugar
• мало времени = little time

Зелень usually means fresh herbs / greens, especially in cooking.

Depending on context, it can refer to things like:

• dill
• parsley
• green onions
• cilantro
• other fresh leafy herbs

So немного зелени is very natural in a food context and means a little fresh herbs / some greens.

Получается is very common in Russian when talking about how food, a dish, or a result turns out.

So:

• салат получается вкуснее = the salad turns out tastier
• more naturally in English: the salad tastes better / comes out tastier

It suggests the result of making the salad with those ingredients.

Compare:

• Салат вкуснее = The salad is tastier
  This is more direct, but less natural for describing the result of preparation.
• Салат становится вкуснее = The salad becomes tastier
  Grammatically fine, but less idiomatic here.
• Салат получается вкуснее = the most natural choice for the salad turns out better

Because Russian comparatives are often built into a single word.

• вкусный = tasty
• вкуснее = tastier / more tasty

So вкуснее already contains the idea of more.

This is similar to English tasty → tastier.

Other examples:

• быстрый → быстрее = fast → faster
• интересный → интереснее = interesting → more interesting
• дорогой → дороже = expensive → more expensive

Russian often leaves the comparison understood from context.

Салат получается вкуснее means:

• The salad turns out tastier
• implied: than without those ingredients or than usual

English does this too sometimes:

• It tastes better with lemon.

You understand: better than without lemon.

If Russian wanted to say it explicitly, it could:

• ...вкуснее, чем без них = ...tastier than without them

But in everyday speech, leaving it implied is very normal.

Russian word order is flexible, but this order sounds natural because it sets the scene first:

• дома = at home
• есть майонез... = there is mayonnaise...

So Если дома есть... feels like:

• If at home there is...
• more naturally: If there is ... at home

You could also hear Если есть дома майонез..., but it sounds a bit less neutral and can put extra focus on майонез.

Russian has no articles like a or the.

So салат can mean:

• salad
• a salad
• the salad

You understand which one is meant from context.
Here it most naturally means the salad or salad in general.

It can feel fairly general, like a cooking tip:

• If there’s mayonnaise, vinegar, and a little greenery at home, the salad turns out tastier.

This sounds like a general statement about making salad, not necessarily one specific salad at one specific moment.

Russian often uses singular nouns this way for general truths:

• Чай вкуснее с лимоном. = Tea tastes better with lemon.
• Суп получается лучше на следующий день. = Soup turns out better the next day.

Because the sentence begins with an если clause:

• Если дома есть майонез, уксус и немного зелени, ...

Russian separates that subordinate clause from the main clause with a comma.

Structure:

• Если ... , салат получается вкуснее.
• If ... , the salad turns out tastier.

This comma is required in standard Russian punctuation.

Yes, that is a very good natural translation.

Possible natural translations include:

• If you have mayonnaise, vinegar, and some herbs at home, the salad tastes better.
• If there is mayonnaise, vinegar, and a little greenery at home, the salad turns out tastier.
• If you’ve got mayonnaise, vinegar, and some fresh herbs at home, the salad comes out better.

The exact English wording can vary, but the Russian structure is natural and idiomatic.