Meine Lehrerin erklärt heute die Rechtschreibung und sagt, dass jedes Komma wichtig ist.

The ending -in marks a female person in many German job or role nouns.

• der Lehrer = male teacher / teacher (masculine form)
• die Lehrerin = female teacher

So meine Lehrerin means my female teacher.

Because Lehrerin is a feminine noun, and the possessive word mein- has to take the correct ending.

Here, Lehrerin is the subject of the sentence, so it is in the nominative case.
For a feminine noun in the nominative, the form is:

• meine Lehrerin

Compare:

• mein Lehrer = my teacher (masculine)
• meine Lehrerin = my teacher (feminine)

Because the subject is meine Lehrerin, which is third person singular: she.

The verb erklären is conjugated in the present tense like this:

• ich erkläre
• du erklärst
• er/sie/es erklärt
• wir erklären
• ihr erklärt
• sie/Sie erklären

So with meine Lehrerin, you use erklärt.

German main clauses normally follow the verb-second (V2) rule. That means the finite verb must be in the second position.

Here the first element is:

• Meine Lehrerin

So the conjugated verb comes next:

• erklärt

Then other information can follow:

• heute die Rechtschreibung

So:

• Meine Lehrerin | erklärt | heute die Rechtschreibung

This is normal German word order.

Yes. That is also correct.

German lets you move different elements into the first position, but the finite verb still stays in second position:

• Meine Lehrerin erklärt heute die Rechtschreibung.
• Heute erklärt meine Lehrerin die Rechtschreibung.

Both are grammatical. The second version puts more emphasis on today.

Rechtschreibung is a feminine noun, so its article is die.

Also, in this sentence it is the direct object of erklärt, so it is in the accusative case.
For feminine singular nouns, the article is:

• nominative: die
• accusative: die

So the form stays the same:

• die Rechtschreibung

Literally, it is made from:

• recht = correct
• Schreibung = writing

So Rechtschreibung is correct writing, which in normal English is spelling or orthography.

Because dass introduces a subordinate clause, and in German subordinate clauses are normally separated by a comma.

So in:

• ... und sagt, dass jedes Komma wichtig ist.

the comma marks the beginning of the clause introduced by dass.

This is standard German punctuation.

Because dass creates a subordinate clause, and in German subordinate clauses the conjugated verb usually goes to the end.

Main clause:

• Meine Lehrerin sagt ...

Subordinate clause:

• dass jedes Komma wichtig ist

So instead of jedes Komma ist wichtig, German changes the order after dass:

• dass jedes Komma wichtig ist

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

This is a very common question.

• das = usually the for a neuter noun, or that/which as a pronoun
• dass = that as a conjunction introducing a clause

In this sentence, dass is correct because it introduces a full clause:

• dass jedes Komma wichtig ist

You cannot replace it here with das.

Because Komma is a neuter noun: das Komma.

In the clause dass jedes Komma wichtig ist, jedes Komma is the subject, so it is in the nominative case.

For jeder- words in the nominative singular:

• masculine: jeder
• feminine: jede
• neuter: jedes

So:

• jedes Komma = every comma

Because all German nouns are capitalized.

So:

• Lehrerin
• Rechtschreibung
• Komma

are all written with capital letters because they are nouns.

Because und normally connects parts of a sentence without needing a comma.

The comma here is not for und. It is there because of dass:

• ... erklärt heute die Rechtschreibung und sagt, dass ...

So:

• no comma before und
• comma before dass

Yes. sagen can introduce reported speech or a statement, and dass gives the content of what is said.

So:

• Sie sagt, dass jedes Komma wichtig ist.

means:

• She says that every comma is important.

The dass-clause functions as the content of sagt.

Because wichtig here is used as a predicate adjective, not as an adjective directly in front of a noun.

Compare:

• das wichtige Komma = the important comma

  • here the adjective is before the noun, so it takes an ending

• das Komma ist wichtig = the comma is important

  • here the adjective comes after sein, so it does not take an ending

In your sentence, it is the second type:

• jedes Komma wichtig ist

So wichtig stays unchanged.

Yes, but that would be a different style and meaning nuance.

• dass jedes Komma wichtig ist = normal everyday statement
• dass jedes Komma wichtig sei = more formal, often used in reported speech or written style

For most learners, ist is the normal and expected form here.

German often uses dass after verbs like:

• sagen
• denken
• glauben
• wissen
• hoffen

to introduce what someone says/thinks/knows.

So:

• Sie sagt, dass jedes Komma wichtig ist.

is a very standard structure.

In spoken German, people sometimes omit dass, but learners should first get comfortable with the full form.

Yes.

In:

• dass jedes Komma wichtig ist

the thing being described as important is jedes Komma, so that is the subject.

You can test it by changing number:

• dass jedes Komma wichtig ist
• dass alle Kommas wichtig sind

The verb changes with the subject, which shows that Komma/Kommas is the subject.