Meine Nachbarin macht ein vegetarisches Gericht mit Zucchini, Paprika und Linsen.

Because Nachbarin is a feminine singular noun.

The possessive word mein- changes its ending depending on gender, number, and case:

• mein Nachbar = my male neighbor
• meine Nachbarin = my female neighbor

Here, Nachbarin is the subject of the sentence, so it is in the nominative case. For a feminine nominative noun, the correct form is meine.

The ending -in is a very common way to make a noun specifically female in German.

• der Nachbar = the male neighbor / the neighbor
• die Nachbarin = the female neighbor

So Nachbarin tells you that the neighbor is a woman.

Yes, in this context machen is very natural. It literally means to make or to do, but German often uses it when talking about preparing food:

• ein Gericht machen = to make a dish
• Abendessen machen = to make dinner

Other verbs are possible too:

• kochen = to cook
• zubereiten = to prepare

So Meine Nachbarin macht ein vegetarisches Gericht is a normal everyday way to say that she is making a vegetarian dish.

Because Gericht is a neuter noun: das Gericht.

It is the direct object of macht, so it is in the accusative case. For neuter nouns, the indefinite article is:

• nominative: ein
• accusative: ein

So the article does not change here.

That is why you get:

• ein Gericht

not

• einen Gericht

The form einen is used for masculine accusative nouns, for example:

• einen Salat

Because it is an adjective before a neuter singular noun with ein.

The noun is Gericht, which is neuter: das Gericht. In the phrase ein vegetarisches Gericht, the adjective has to take the correct ending for that pattern.

So:

• ein vegetarisches Gericht

This is part of German adjective endings, which depend on:

• gender
• case
• whether there is an article like der, die, das, or ein

You do not need to memorize the whole system from this sentence alone, but here the important point is:

• neuter singular + ein + adjective + noun
  gives ein vegetarisches Gericht

Because German often leaves out articles when talking about ingredients in a general sense.

So:

• mit Zucchini, Paprika und Linsen

sounds like a normal ingredient list, similar to English with zucchini, bell pepper, and lentils.

If you wanted to be more specific, articles could appear, for example:

• mit der Zucchini und den Linsen

But in ordinary recipe-style wording, no article is very common.

Mit always takes the dative case.

So anything after mit is grammatically in the dative:

• mit der Nachbarin
• mit dem Gericht
• mit den Linsen

In your sentence, the nouns after mit do not have articles, so the dative is not very visible on the surface:

• mit Zucchini, Paprika und Linsen

But the preposition still requires dative.

Linsen is clearly plural.

The other two are a little trickier because ingredient nouns are often used in a more general way:

• Zucchini can be singular or plural in form, depending on context
• Paprika is often used as an ingredient noun without an article, so number is not strongly emphasized here

In this sentence, the main idea is simply that the dish contains those ingredients. German often does not force you to make the number as explicit in ingredient lists as English learners might expect.

That final part is a prepositional phrase that gives extra information about the dish: what it is made with.

The basic sentence is:

• Meine Nachbarin macht ein vegetarisches Gericht.

Then German adds:

• mit Zucchini, Paprika und Linsen

Putting that kind of detail after the object is very normal. German word order is flexible in some ways, but this placement is natural and straightforward.

Because in German, all nouns are capitalized.

That includes:

• Nachbarin
• Gericht
• Zucchini
• Paprika
• Linsen

This is one of the most noticeable differences from English writing. Adjectives and verbs are normally not capitalized unless they begin the sentence.