Det är först när jag sitter på balkongen som jag känner mig lugn.

This is an emphatic structure, often called a cleft sentence.

The more neutral version would be:

Jag känner mig lugn först när jag sitter på balkongen.

The actual sentence:

Det är först när jag sitter på balkongen som jag känner mig lugn.

puts special focus on först när jag sitter på balkongen. In English, it works a lot like:

It is only when I sit on the balcony that I feel calm.

So the structure is not necessary, but it adds emphasis.

Here, först does not mean first in the sense of before other things.

In the pattern först när, it usually means:

• only when
• not until

So:

Det är först när ... som ...

means something like:

It is only when ... that ...

or

It is not until ... that ...

This is a very common Swedish pattern.

In this sentence, som is part of the emphatic det är ... som ... structure.

So:

• Det är först när jag sitter på balkongen = the focused part
• som jag känner mig lugn = the rest of the statement

It functions a bit like English that in:

It is only when I sit on the balcony that I feel calm.

So som here is not really something you translate word-for-word every time; it is part of the sentence pattern.

När means when, and om means if.

Swedish uses när here because the speaker is talking about a real situation or repeated experience:

när jag sitter på balkongen = when I’m sitting on the balcony

If you used om, it would sound more hypothetical:

• Om jag sitter på balkongen ... = If I sit on the balcony ...

So när fits better because this is about the condition under which the speaker actually feels calm.

Because sitter gives more specific information: the speaker is sitting on the balcony, not just located there.

Swedish often uses posture verbs more naturally than English does:

• sitta = sit
• stå = stand
• ligga = lie
• vara = be

So:

• jag är på balkongen = I am on the balcony
• jag sitter på balkongen = I am sitting on the balcony

The version with sitter paints a clearer picture and sounds very natural.

Swedish normally uses på with balkong:

• på balkongen = on the balcony / out on the balcony

That is just the usual idiomatic preposition.

Using i balkongen would sound strange in normal speech, because it suggests being inside the physical structure of the balcony rather than out on it.

So this is a case where you mainly need to learn the preposition as part of the expression:

sitta på balkongen

Känna sig + adjective means to feel + adjective.

So:

• jag känner mig lugn = I feel calm
• jag är lugn = I am calm

The difference is similar to English:

• feel calm = describes the speaker’s inner experience
• be calm = describes the state more directly or objectively

In this sentence, the speaker is talking about a personal feeling, so känner mig lugn is the natural choice.

Because Swedish uses the reflexive pattern känna sig for feel when talking about your own state.

So:

• jag känner mig lugn = I feel calm
• hon känner sig trött = she feels tired
• de känner sig trygga = they feel safe

Without sig/mig/dig/osv., känna usually means to know a person or to feel something physically with the senses:

• Jag känner Anna. = I know Anna.
• Jag känner vinden. = I feel the wind.

So mig is necessary here.

Because the adjective agrees with the person who feels that way, in this case jag.

With jag, the basic common-gender form is used:

• Jag känner mig lugn.
• Han känner sig trött.
• Hon känner sig glad.

You would use -t with a neuter subject such as det:

• Det känns lugnt. = It feels calm / It feels okay.

And you would use -a in plural:

• Vi känner oss lugna.

So lugn is correct because the subject is jag.

Because both när and som introduce subordinate clauses here, and subordinate clauses in Swedish do not follow the usual main-clause V2 pattern.

So you get:

• när jag sitter på balkongen
• som jag känner mig lugn

not:

• när sitter jag ...
• som känner jag ...

This is an important pattern in Swedish: in subordinate clauses, the subject normally comes before the finite verb.

Yes. That sentence is correct and natural.

Compare:

• Jag känner mig lugn först när jag sitter på balkongen.
  More neutral.

• Det är först när jag sitter på balkongen som jag känner mig lugn.
  More emphatic; it highlights the condition.

So the meaning is basically the same, but the original sentence gives stronger focus to only when I’m sitting on the balcony.