Die Lehrerin bestraft das Kind nicht.

Because German nouns have grammatical gender.

• Lehrerin is a feminine noun, so it takes die in the nominative singular.
• Kind is a neuter noun, so it takes das.

This is not about whether the child is biologically male or female. In German, Kind is simply a neuter noun, so its article is das.

The ending -in is a very common way to make a feminine noun for a person.

• der Lehrer = male teacher
• die Lehrerin = female teacher

So Lehrerin specifically means a female teacher. If the teacher were male, the sentence would begin with Der Lehrer.

It is in the nominative case, because it is the subject of the sentence — the person doing the action.

In this sentence, die Lehrerin is the one carrying out bestraft, so it is nominative.

It is in the accusative case, because it is the direct object — the person or thing receiving the action.

The teacher is doing something to the child, so das Kind is accusative.

Because for many neuter nouns in German, the article is the same in both cases:

• nominative singular: das Kind
• accusative singular: das Kind

So even though the case changes, the form does not change here.

Because German verbs are conjugated to match the subject.

The infinitive is bestrafen.
With die Lehrerin = she / it (third person singular), the verb becomes:

• ich bestrafe
• du bestrafst
• er/sie/es bestraft

So die Lehrerin bestraft is the correct form.

In a normal German main clause, the finite verb usually comes in second position.

Here the sentence structure is:

• Die Lehrerin = first element
• bestraft = second position
• das Kind nicht = the rest of the sentence

This is one of the most important word-order rules in German.

Here nicht negates the verb idea / the whole action: the teacher does not punish the child.

German often puts nicht late in the clause, especially when it is negating the main action and there is no second verb at the end.

So:

• Die Lehrerin bestraft das Kind nicht.

is the natural way to say that the action does not happen.

No. That word order is incorrect in a normal main clause.

The conjugated verb must stay in second position, so bestraft has to come right after the first element:

• correct: Die Lehrerin bestraft das Kind nicht.
• incorrect: Die Lehrerin nicht bestraft das Kind.

Yes, but it changes the emphasis.

• Die Lehrerin bestraft das Kind nicht.
  = neutral statement: the teacher does not punish the child.

• Die Lehrerin bestraft nicht das Kind.
  = stronger contrast, something like: the teacher punishes not the child (but perhaps someone else).

So the original sentence is the more neutral, standard version.

Because all nouns are capitalized in German.

So:

• die Lehrerin
• das Kind

Both nouns begin with a capital letter, no matter where they appear in the sentence.

It corresponds to the, but German articles carry more grammatical information than English ones.

die tells you things like:

• the noun is singular feminine here
• the noun is in the nominative case in this sentence

So while English just has the, German changes the article depending on gender, number, and case.

Yes. It follows a very common basic pattern:

• Die Lehrerin = subject
• bestraft = verb
• das Kind = object
• nicht = negation

So for an English speaker, the overall structure is fairly familiar, even though German has stricter rules about verb position and negation placement.