Beim Mitschreiben merke ich, dass ich über schwierige Fragen länger nachdenken muss.

Beim is a contraction of bei dem.

In this sentence, beim + nominalized verb is a very common German way to mean while doing something.

• beim Mitschreiben = while taking notes
• literally, something like during the note-taking

So German uses a noun-like form here instead of a full clause such as while I am taking notes.

A full alternative would be:

• Während ich mitschreibe, ...

but beim Mitschreiben is shorter and very natural.

Because it is being used as a noun here.

German can turn verbs into nouns very easily. When that happens, they are capitalized.

• mitschreiben = to take notes / to write along
• das Mitschreiben = the act of taking notes

After beim in this kind of structure, German often uses this noun form:

• beim Lesen = while reading
• beim Essen = while eating
• beim Mitschreiben = while taking notes

Because German puts the finite verb in second position in a main clause.

The first position can be taken by many things, not just the subject. Here, Beim Mitschreiben comes first for emphasis or flow.

So the pattern is:

• Beim Mitschreiben = position 1
• merke = position 2
• ich = then the subject comes after the verb

Both of these are correct:

• Beim Mitschreiben merke ich, dass ...
• Ich merke beim Mitschreiben, dass ...

The first version gives a bit more emphasis to while taking notes.

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

So:

• Ich merke, dass ... = I notice/realize that ...

This comma is not optional in standard German.

Because the sentence contains two clauses, and each clause needs its own subject.

Main clause:

• Beim Mitschreiben merke ich

Subordinate clause:

• dass ich über schwierige Fragen länger nachdenken muss

Even though both clauses refer to the same person, German still says ich again.

English does the same thing:

• I notice that I need to think longer ...

You would not normally say:

• I notice that need to think longer ...

German works the same way here.

Because the part after dass is a subordinate clause, and in German subordinate clauses, the verb goes to the end.

Here the verb structure is:

• nachdenken müssen = to have to think

In the dass clause, that verbal part moves to the end:

• ..., dass ich über schwierige Fragen länger nachdenken muss.

That is very typical German subordinate-clause word order.

Compare:

• Main clause: Ich muss über schwierige Fragen länger nachdenken.
• Subordinate clause: ..., dass ich über schwierige Fragen länger nachdenken muss.

Yes, nachdenken is a separable verb.

In a normal main clause with a finite form, it splits:

• Ich denke über schwierige Fragen nach.

But when it appears as an infinitive, it stays together:

• Ich muss über schwierige Fragen nachdenken.

And in your sentence, it is an infinitive inside a subordinate clause:

• ..., dass ich über schwierige Fragen länger nachdenken muss.

So the nach does not move away here.

The verb expression is:

• über etwas nachdenken = to think about something

So nachdenken commonly takes über + accusative.

That means:

• über schwierige Fragen

is in the accusative plural.

Here, schwierige Fragen means difficult questions in a general sense, without a definite article.

Compare:

• über schwierige Fragen = about difficult questions
• über die schwierigen Fragen = about the difficult questions

The second one would sound more specific.

Because German often leaves out the article when speaking about things in a general, non-specific way.

So:

• über schwierige Fragen nachdenken = think about difficult questions

This sounds general: difficult questions as a category.

If you add an article, it becomes more specific:

• über die schwierigen Fragen nachdenken = think about the difficult questions

That would usually refer to particular questions already known in the context.

Länger is the comparative form of lange and here it means:

• for longer
• for a longer time

So the idea is not necessarily longer in physical length, but more time.

In this sentence, the comparison is implied. It means something like:

• I need more time to think about difficult questions
• I need to think about difficult questions longer than about easier ones

German often uses this kind of comparative without stating the full comparison explicitly.

Yes, but they are not exactly the same.

• Beim Mitschreiben = while taking notes / during note-taking
• Während ich mitschreibe = while I am taking notes

These are very close in meaning. Beim Mitschreiben is just more compact.

But:

• Wenn ich mitschreibe = when / whenever I take notes

That can sound more like a repeated situation or condition, not simply an action happening at the same time.

So for this sentence, beim Mitschreiben or während ich mitschreibe are the closest matches.