Nach jeder Besprechung mache ich eine kurze Notiz.

Because nach is a preposition that takes the dative case when it means after.

• die Besprechung = the meeting/discussion
• Dative singular becomes der Besprechung
• With jeder in the feminine dative singular, you get jeder

So:

• nominative: jede Besprechung
• dative after nach: nach jeder Besprechung

Here jeder means every.

It changes its ending to match the noun’s:

• Besprechung is feminine
• it is singular
• it is in the dative case because of nach

That is why the form is jeder.

Compare:

• jeder Tag = every day
• jede Besprechung = every meeting
• nach jeder Besprechung = after every meeting

German uses the singular after jeder/jede/jedes just like English does after every.

So:

• every meeting → singular
• jede Besprechung → singular

If you used the plural, it would mean something different, more like after all meetings or after meetings depending on the wording.

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

The sentence starts with a time phrase:

• Nach jeder Besprechung = after every meeting

Since that phrase comes first, the verb must still stay second:

• Nach jeder Besprechung mache ich ...

So the structure is:

• time expression
  • verb
    • subject
      • rest

This is a very common German word order pattern.

Because when something other than the subject comes first, German usually inverts the subject and verb.

So:

• neutral order: Ich mache nach jeder Besprechung eine kurze Notiz.
• with emphasis on time: Nach jeder Besprechung mache ich eine kurze Notiz.

In both sentences, the verb is still in second position.

This is the direct object of the verb machen, so it is in the accusative case.

• Notiz is feminine: die Notiz
• feminine accusative article is eine
• after eine, the adjective kurz takes the ending -e

So:

• eine kurze Notiz = a short note

Because German adjectives change their endings depending on the article, gender, number, and case.

Here:

• Notiz is feminine
• singular
• accusative
• it has the article eine

So the adjective takes the ending -e:

• eine kurze Notiz

Other examples:

• ein kurzer Text = a short text
• eine kurze Notiz = a short note
• ein kurzes Gespräch = a short conversation

Yes, eine Notiz machen is natural and understandable. It means to make a note.

You may also hear:

• sich eine Notiz machen = to make oneself a note
• etwas notieren = to note something down
• etwas aufschreiben = to write something down

So this sentence is perfectly normal, but there are several common alternatives.

Eine Notiz machen simply says you make a note.

Mir eine Notiz machen adds the idea that you are making the note for yourself.

For example:

• Ich mache eine Notiz. = I make a note.
• Ich mache mir eine Notiz. = I make myself a note / I jot something down for myself.

Both are common. The version with mir often sounds a little more personal or idiomatic.

Not always exactly, but it is often a good translation.

Besprechung usually suggests a discussion, consultation, or meeting where things are talked through. Depending on context, English might use:

• meeting
• discussion
• briefing
• consultation

So in many workplace contexts, Besprechung = meeting is a very natural translation.

Yes, but the meaning changes.

• Nach jeder Besprechung = after every meeting
• Nach der Besprechung = after the meeting

So jeder makes it a habitual or repeated action, while der refers to one specific meeting.

Yes. That is also correct.

The difference is mainly emphasis:

• Ich mache nach jeder Besprechung eine kurze Notiz.
  More neutral, starts with I.

• Nach jeder Besprechung mache ich eine kurze Notiz.
  Emphasizes when you do it.

German often moves time expressions to the front when they are important in the sentence.

It sounds completely natural.

In speech, nach jeder Besprechung is often pronounced quite smoothly, and the stress may fall on different parts depending on emphasis:

• Nach jeder Besprechung mache ich eine kurze Notiz.
  Emphasis on the routine: after every meeting

• Nach jeder Besprechung mache ich eine kurze Notiz.
  Emphasis on I

• Nach jeder Besprechung mache ich eine kurze Notiz.
  Emphasis on what exactly you do

So the sentence is both grammatically correct and idiomatic in everyday German.