Im Wörterheft notiere ich auch Wörter zu meiner eigenen Herkunft und Familie, damit ich darüber frei sprechen kann.

Im is just the contracted form of in dem.

• in dem Wörterheft → im Wörterheft
• This happens very often in German:
  
  • in dem → im
  • an dem → am
  • bei dem → beim, etc.

So Im Wörterheft literally means In the vocabulary notebook. The writer just uses the normal, shortened form.

If you wanted to say in my vocabulary notebook, you would say In meinem Wörterheft, not im Wörterheft.

The preposition in can take either dative or accusative, depending on the meaning:

• Dative = location (where something is)
• Accusative = movement (where something is going)

Here, Im Wörterheft notiere ich … describes where the writing happens, not movement into the notebook. So it is a static location:

• Wo? (Where?) → im Wörterheft → dative
• If it were movement: Ich schreibe die Wörter ins Wörterheft. (ins = in das, accusative)

German likes to form compounds by joining nouns:

• Wörter (words) + Heft (notebook) → Wörterheft (vocabulary notebook)

All nouns in German are capitalized, so Wörterheft must be capitalized.
Because it is a single compound noun, it’s written as one word, not Wörter Heft.

German main clauses normally follow a verb‑second (V2) rule: the conjugated verb must be in position 2. Everything else can be moved around for emphasis.

Two correct possibilities are:

• Im Wörterheft (position 1) notiere (position 2) ich auch Wörter …
• Ich (position 1) notiere (position 2) im Wörterheft auch Wörter …

In the given sentence, the speaker wants to emphasize where they write the words, so Im Wörterheft is put in the first position, and then the verb notiere still stays in second place, forcing ich to come after the verb.

Auch means also / as well. It tells us that the person writes down not only other kinds of words, but also words about their own background and family.

Its position is:

• after the conjugated verb (notiere)
• before the direct object (Wörter)

You could move it slightly, but the meaning changes in nuance:

• Ich notiere auch Wörter … (neutral: I also write down words …)
• Ich notiere Wörter auch … (could emphasize that the writing down also happens, in addition to something else)

The given position notiere ich auch Wörter is the most natural and neutral here.

German distinguishes:

• Wörter = individual, countable words, as items in a list or vocabulary
• Worte = words as a connected expression, statement, or saying

Examples:

• Ich lerne neue Wörter. → vocabulary items
• Seine letzten Worte waren … → his last (spoken) words as a meaningful whole

In Im Wörterheft notiere ich auch Wörter …, we are clearly talking about vocabulary items written in a notebook, so Wörter is correct.

The preposition zu always takes the dative case, no exceptions.

• zu
  • meiner eigenen Herkunft (feminine, dative singular)
• (zu) meiner Familie (also dative, sharing the same zu)

The forms:

• meine Herkunft (nominative) → zu meiner Herkunft (dative)
• eigene agrees with Herkunft and in dative feminine singular takes -en: meiner eigenen Herkunft

So the structure is: Wörter zu meiner eigenen Herkunft und (zu) meiner Familie = words relating to my own origin and (to) my family.

Both versions are grammatically correct:

• zu meiner eigenen Herkunft und Familie
• zu meiner eigenen Herkunft und meiner Familie

German often avoids repeating the same determiner if it clearly applies to both nouns. So meiner is understood to belong to both Herkunft and Familie.

Adding meiner before Familie makes the structure a bit heavier, but can slightly emphasize that the family is also my family. In everyday language, dropping the second meiner as in the original sentence is very natural.

Herkunft basically means origin / background, especially:

• where you come from
• your ethnic, cultural, or social background
• family roots

Heimat has a more emotional and cultural meaning: home, homeland, the place or environment you feel you belong to.

So in this sentence, meine eigene Herkunft suggests my own origins / background (e.g., country, culture, maybe migration background), not just the place that feels like home.

Damit introduces a purpose clause: it means so that / in order that.

• Ich notiere Wörter, damit ich darüber frei sprechen kann.
  → I write down words so that I can speak freely about it.

Difference from similar words:

• deshalb = therefore / for that reason and does not create a subordinate clause:
  
  • Ich notiere Wörter. Deshalb kann ich darüber frei sprechen.
• um … zu also expresses purpose but is used when the subject is the same in both parts, and it doesn’t take dass- / damit- word order:
  
  • Ich notiere Wörter, um darüber frei sprechen zu können.

Here damit + full clause gives a clear, slightly more formal expression of purpose.

Darüber is a da‑compound: da + über. It means about it / about that and refers back to meiner eigenen Herkunft und Familie.

German often uses da + preposition instead of a pronoun + preposition when referring to things that were just mentioned:

• Wörter zu meiner eigenen Herkunft und Familie
  → darüber (about that)

If you said über sie, it would sound more like about them and could be misread as referring only to the people (e.g., the family members) rather than the whole topic of origin and family as a subject. Darüber is the natural, neutral choice here.

Because damit introduces a subordinate clause, the conjugated verb must go to the end of that clause.

With a modal verb (können) and a main verb (sprechen), the order in a subordinate clause is:

1. Other elements (subject, objects, adverbs, etc.)
2. Main verb in infinitive (sprechen)
3. Modal verb (kann) right at the end

So:

• … damit ich darüber frei sprechen kann.

In a main clause, the order would be different:

• Ich kann darüber frei sprechen. (verb‑second: kann is in position 2)