Learn Hardcore German: Zwischen den Terminen lerne ich im Selbststudium mit Videos und Podcasts weiter. - Between appointments I continue learning in self-study with videos and podcasts.

In this sentence, the meaning is “in the time between the appointments”, i.e. a time location, not a movement into that space.
So you need the dative plural form:

nominative plural: die Termine
dative plural: den Terminen

Hence: Zwischen den Terminen.

What is the grammatical function of Zwischen den Terminen in this sentence?

Zwischen den Terminen is a prepositional phrase functioning as an adverbial of time (“when?”).

The basic structure of the sentence is:

lerne ich weiter = I continue studying / I keep learning

Then we add:

Zwischen den Terminen → tells you when this happens
im Selbststudium → tells you how / in what manner you study
mit Videos und Podcasts → tells you with what resources you study

So Zwischen den Terminen is not the subject; it’s a time expression at the beginning of the sentence.

Why is the word order Zwischen den Terminen lerne ich ... and not Ich lerne zwischen den Terminen ...?

Both are correct:

Zwischen den Terminen lerne ich …
Ich lerne zwischen den Terminen …

German main clauses obey the verb-second rule (V2):

One element in the first position (can be subject, time, object, etc.).
The conjugated verb must be in second position.
The rest of the elements follow.

In your sentence, the first position is taken by the time phrase Zwischen den Terminen, so the verb lerne must come second, and the subject ich comes after the verb:

Zwischen den Terminen → position 1
lerne → position 2 (V2)
ich ... → everything else

If you start with ich, you still keep the verb second:

Ich (1) lerne (2) zwischen den Terminen …

What exactly does weiter lernen / lerne … weiter mean?

weiterlernen literally means “to continue learning” / “to keep studying”.

In the sentence it’s split:

lerne … weiter = “continue to learn / study further”

weiter here is a separable prefix:

infinitive: weiterlernen
main clause: ich lerne weiter
past: ich habe weitergelernt

The idea is: I was already learning earlier (e.g. in lessons, during appointments), and zwischen den Terminen I don’t stop; I continue on my own.

Why is weiter at the very end of the sentence?

Because weiterlernen is a separable verb (verb with a separable prefix).

For separable verbs in a main clause:

the conjugated verb goes to position 2
the prefix goes to the end of the clause

So:

infinitive: weiterlernen
main clause: ich lerne … weiter

Your sentence has extra information between the verb and the prefix:

lerne ich im Selbststudium mit Videos und Podcasts weiter

But weiter still stays at the very end of the clause, after all objects and adverbials.

What does im Selbststudium mean, and why im?

Selbststudium means self-study; studying by yourself, independently.

im is the contraction of in dem:

in (preposition) + dem (dative neuter article) → im

Selbststudium is a neuter noun:

das Selbststudium → in dem Selbststudium → im Selbststudium

Grammatically:

im Selbststudium is a prepositional phrase in the dative.
Function: it describes the manner / way in which you learn: “in self-study” / “through self-study”.

Why is it mit Videos und Podcasts and not mit Video und Podcast?

Because the speaker is talking about using multiple videos and podcasts in general, not a single one of each.

Video → singular
Videos → plural
der Podcast (sg.) → die Podcasts (pl.)

The preposition mit always takes the dative case, including for plurals, but in the weak plural of these loanwords, the form looks the same as nominative plural:

nominative plural: die Videos, die Podcasts
dative plural: mit Videos, mit Podcasts
(no extra -n is added here)

So mit Videos und Podcasts = with videos and podcasts (in general / several of them).

Why is Selbststudium capitalized?

In German, all nouns are capitalized, regardless of position in the sentence.

Selbststudium is a noun (like “study” in the sense of “course of study / act of studying”), so it must be written with a capital letter:

das Selbststudium

This is independent of any special status; it’s just the standard rule: every noun, always capital.

Could I say Ich studiere im Selbststudium … instead of Ich lerne …? What’s the difference between lernen and studieren?

You could say it, but it often sounds a bit odd or too formal in this context.

Basic difference:

lernen = to learn / to study (very broad; for school, languages, skills, etc.)
studieren = to study at a university (be enrolled in a degree program) or to study something in depth (more academic / focused)

Examples:

Ich lerne Deutsch. → natural, everyday German.
Ich studiere Deutsch. → I’m a university student in German studies.

In the sentence:

Zwischen den Terminen lerne ich im Selbststudium …
→ sounds perfectly natural: “I keep studying (by myself) between the appointments.”

Ich studiere im Selbststudium … is grammatically fine, but can sound redundant or stylistically heavy; most native speakers would prefer lerne here.

Is Zwischen den Terminen only about time, or can it also mean a physical “between”?

In this sentence it’s purely temporal (about time): between appointments → in the intervals between scheduled meetings.

But zwischen itself is used for both:

Spatial:
- zwischen den Häusern = between the houses
Temporal:
- zwischen den Terminen = between the appointments (in time)

Context tells you whether it’s a physical space or a time span. Here, it clearly refers to the time gaps between appointments.

How would this sentence change in the past tense?

Use the Perfekt (common spoken past), keeping the separable verb pattern:

Present:

Zwischen den Terminen lerne ich im Selbststudium mit Videos und Podcasts weiter.

Perfekt:

Zwischen den Terminen habe ich im Selbststudium mit Videos und Podcasts weitergelernt.

Changes:

lerne … weiter → habe … weitergelernt
- auxiliary: haben
- past participle of weiterlernen: weitergelernt (prefix + ge + stem + t)

Why is ich not at the very beginning of the sentence like in English (“Between the appointments I learn…” vs. “I learn between the appointments…”)? Is starting with a time phrase common?

Starting a sentence with a time expression is very common and stylistically natural in German.

German word order is quite flexible; as long as the verb is in second position, you can move elements to the front to emphasize them. Putting Zwischen den Terminen first emphasizes when something happens.

All of these are correct, but the nuance changes slightly:

Zwischen den Terminen lerne ich … → focus on between the appointments
Ich lerne zwischen den Terminen … → neutral, focus more on ich lerne
Im Selbststudium lerne ich zwischen den Terminen weiter. → focus on self-study

So yes, beginning with time phrases (or place, or other adverbials) is very typical in German.