Learn Hardcore German: Wenn Arbeit, Familie und Freizeit im Gleichgewicht sind, fühle ich mich innerlich ruhiger. - When work, family, and free time are in balance, I feel calmer inside.

Here, the meaning is a general condition: Whenever / If work, family and free time are in balance, I feel calmer inside. That’s exactly what wenn is for.

wann would be wrong because this is not a question.
als would suggest one specific past time, which doesn’t fit the general, timeless condition here.

Why is the verb sind at the end of the wenn-clause?

In German, subordinate clauses (introduced by words like wenn, weil, dass, obwohl, etc.) send the conjugated verb to the end.

So:

Main clause: Arbeit, Familie und Freizeit sind im Gleichgewicht. (Verb in 2nd position)
Subordinate clause with wenn: Wenn Arbeit, Familie und Freizeit im Gleichgewicht sind, … (verb to the end)

Word order rule:

Subordinate clause: conjunction – subject – (other stuff) – verb

So it becomes:

Wenn (conjunction)
Arbeit, Familie und Freizeit (subject)
im Gleichgewicht (adverbial phrase)
sind (verb at the end)

Why does the main clause start with fühle and not ich fühle?

The wenn-clause comes first:

Wenn Arbeit, Familie und Freizeit im Gleichgewicht sind, …

When a subordinate clause comes first, German usually inverts the word order in the following main clause: the finite verb must stay in 2nd position overall.

So we get:

Wenn … sind, fühle ich mich innerlich ruhiger.

Here, in the main clause:

First element: the entire wenn-clause
Second element: fühle (the finite verb)
Then: ich
Then: the rest (mich innerlich ruhiger)

If you moved ich before fühle, you’d break the verb-second rule for the main clause. So fühle ich is the correct inversion.

Why is it fühle ich mich and not just ich fühle?

In German, sich fühlen is usually reflexive when it means to feel (in a certain state).

Ich fühle mich gut. = I feel good.
Er fühlt sich krank. = He feels ill.
Fühle ich mich innerlich ruhiger. = I feel calmer inside.

Without mich, fühlen tends toward “to feel (something with your senses)”:

Ich fühle die Kälte. = I feel the cold.
Ich fühle den Schmerz. = I feel the pain.

Here, we are describing my state, so German needs the reflexive form: > ich fühle mich …

Why is it ruhiger and not just ruhig?

ruhiger is the comparative form of ruhig.

ruhig = calm
ruhiger = calmer (more calm)

The sentence describes feeling more calm than usual / than before, not just calm in an absolute sense:

… fühle ich mich innerlich ruhiger.
= I feel calmer inside.

If you said:

Ich fühle mich innerlich ruhig.
→ I feel calm inside (no comparison, just a state).

With ruhiger, there is an implied comparison to a less calm state in other situations.

What does innerlich mean here, and why not innerer or something similar?

innerlich is an adjective/adverb meaning inner, internal, inward(ly).

In this sentence, it functions adverbially, describing how you feel calmer:

fühle ich mich innerlich ruhiger
= I feel calmer inside / inwardly / on the inside.

We don’t say innerer here because:

We are not attributing it directly to a noun (like der innere Frieden = the inner peace).
We are qualifying the manner of the feeling, so the adverb-like form innerlich is used.

Why is it im Gleichgewicht and not in Gleichgewicht or something like in Balance?

im = in dem (in the), contracted.

im Gleichgewicht sein is a fixed and very common expression meaning:

to be in balance / in equilibrium

So:

Arbeit, Familie und Freizeit sind im Gleichgewicht.
= Work, family and leisure are in balance.

in Gleichgewicht (without article) is not idiomatic here; German normally uses the article dem → im.

in Balance is influenced by English “in balance” and is less idiomatic in this context. Native speakers will usually say im Gleichgewicht for the idea of a balanced state in life, work, etc.

What case are Arbeit, Familie und Freizeit in?

They are in the nominative case because they form the subject of the verb sind.

Wer oder was ist im Gleichgewicht?
→ Arbeit, Familie und Freizeit
→ Subject → nominative

Even though it’s a list of three things, together they act as one compound subject in the nominative case.

Why is it sind and not ist?

The subject is plural:

Arbeit, Familie und Freizeit = three elements → plural subject.

The verb must agree in number, so we need the 3rd person plural:

ist = he/she/it is (3rd singular)
sind = they are (3rd plural)

So:

Die Arbeit ist wichtig. (singular)
Arbeit, Familie und Freizeit sind wichtig. (plural)
Arbeit, Familie und Freizeit sind im Gleichgewicht. (plural)

What exactly does Gleichgewicht mean?

das Gleichgewicht literally means equilibrium, balance.

Physical: Das Glas ist im Gleichgewicht. = The glass is in balance / stable.
Figurative, like here: a balanced state between aspects of life.

In this sentence, im Gleichgewicht sein suggests:

none of the three (work, family, free time) is dominating too much
they are in a healthy proportion to each other.

Could I say bin ich innerlich ruhiger instead of fühle ich mich innerlich ruhiger?

Yes, grammatically you can say:

Wenn Arbeit, Familie und Freizeit im Gleichgewicht sind, bin ich innerlich ruhiger.

This is correct and understandable.

Nuance:

bin ich innerlich ruhiger = focuses on being calmer as a state.
fühle ich mich innerlich ruhiger = focuses more on your subjective perception of that state (I feel calmer).

Both work; fühle ich mich … just highlights the felt experience a bit more.

Why is the word order fühle ich mich innerlich ruhiger and not ich fühle mich ruhiger innerlich?

German has relatively flexible word order for adverbials, but there are preferences.

In:

fühle ich mich innerlich ruhiger

the order is:

fühle – verb (must be in 2nd position in the main clause)
ich – subject
mich – reflexive pronoun
innerlich – adverb (manner: inwardly)
ruhiger – predicate adjective (the state)

Putting innerlich directly before ruhiger is natural: it closely modifies the way you are calmer: calmer on the inside.

You might sometimes hear variants like ich fühle mich ruhiger innerlich, but it sounds a bit marked or poetic. The given order (innerlich ruhiger) is the most natural and idiomatic here.