Nach dem Essen tut mein Magen nicht mehr weh.

Because nach takes the dative case when it means after in a time expression.

• das Essen = nominative/accusative
• dem Essen = dative

So:

• nach dem Essen = after the meal / after eating

This is a very common pattern:

• nach dem Unterricht = after class
• nach der Arbeit = after work
• nach dem Film = after the movie

Because here Essen is being used as a noun, not as a verb.

German capitalizes all nouns. Compare:

• essen = to eat (verb)
• das Essen = the meal / the eating (noun)

In nach dem Essen, it means something like after the meal or after eating, so it is treated as a noun.

It can mean either one, depending on context.

In everyday German, das Essen can refer to:

• the meal itself
• the act of eating

So nach dem Essen can naturally be understood as:

• after the meal
• after eating

Usually the context makes it clear, and in many situations the difference is not important.

Because weh tun / wehtun is the expression German uses for to hurt.

In a main clause, the conjugated verb goes in second position, and the other part appears later:

• Mein Magen tut weh. = My stomach hurts.

When another element comes first, the verb still stays in second position:

• Nach dem Essen tut mein Magen nicht mehr weh.

So:

• tut = the conjugated verb
• weh = the remaining part of the expression, placed at the end

Because the subject is mein Magen, which is third person singular.

The verb tun is conjugated like this here:

• ich tue
• du tust
• er/sie/es tut

Since mein Magen = my stomach = it, you need tut:

• Mein Magen tut weh.

The subject is mein Magen.

You can tell because it is the thing doing the verb grammatically, and the verb agrees with it:

• mein Magen = singular
• tut = singular

So the basic structure is:

• Mein Magen tut weh. = My stomach hurts.

The phrase nach dem Essen is just giving the time context.

German often puts a time phrase first to set the scene.

The important rule is that in a normal main clause, the conjugated verb must be in second position. So if Nach dem Essen comes first, the verb comes next:

• Nach dem Essen tut mein Magen nicht mehr weh.

If you start with the subject instead, that is also possible:

• Mein Magen tut nach dem Essen nicht mehr weh.

Both are grammatical. The version with Nach dem Essen first gives a little more emphasis to the time phrase.

Nicht mehr means no longer or not anymore.

So:

• Mein Magen tut nicht mehr weh. = My stomach doesn’t hurt anymore.

This is a very useful expression. Compare:

• nicht mehr = no longer / not anymore
• noch nicht = not yet

For example:

• Ich bin nicht mehr müde. = I’m not tired anymore.
• Ich bin noch nicht müde. = I’m not tired yet.

That contrast is very important in German.

Because weh tun functions as the verbal idea here, and nicht mehr negates the situation of the stomach hurting.

German often places nicht before the part it is negating, and with expressions like weh tun, the negation naturally comes before weh:

• Mein Magen tut nicht mehr weh.

That is the normal, idiomatic order.

Because mein already works as a determiner.

In German, you normally use either:

• an article: der Magen = the stomach
• or a possessive: mein Magen = my stomach

You do not normally combine them like der mein Magen.

Also, Magen is a masculine noun:

• der Magen

That is why you would say:

• mein Magen
• der Magen

Yes. Mein Magen is in the nominative because it is the subject of the sentence.

So the cases in this sentence are:

• nach dem Essen → dative, because of nach
• mein Magen → nominative, because it is the subject

This is a good example of how one sentence can contain more than one case.

Yes, that is grammatically correct, but it sounds a bit less everyday.

• weh tun is very common in normal spoken German
• schmerzen is a bit more formal or literary

So in everyday speech, Mein Magen tut weh is usually the more natural choice.

Yes, very often.

Examples:

• Mein Kopf tut weh. = My head hurts.
• Mein Rücken tut weh. = My back hurts.
• Mein Arm tut weh. = My arm hurts.
• Meine Augen tun weh. = My eyes hurt.

Notice that with a plural subject, the verb changes:

• Meine Augen tun weh.
• not Meine Augen tut weh

So the verb must always agree with the subject.

Yes. You will often see the infinitive written as wehtun.

But in a main clause, the parts are separated in the usual way:

• infinitive: wehtun
• main clause: Mein Magen tut weh.

So for learners, the most important thing is to recognize that the dictionary form may appear as wehtun, but in the sentence it shows up as tut ... weh.