Learn Hardcore Finnish: Minun äidinkieleni on ruotsi.

So minun äidinkieleni is literally my mother tongue-my. In normal speech and writing you almost always use either the pronoun or the suffix, and the suffix is obligatory if there is no other possessor shown.

Therefore:

Äidinkieleni on ruotsi. = My native language is Swedish. (no pronoun, just suffix)
Minun äidinkieleni on ruotsi. = fully explicit, a bit more emphatic: My native language is Swedish.

Can I just say Minun äidinkieli on ruotsi without the -ni?

No, that sounds ungrammatical or at least very odd. If you show the possessor with minun, Finnish still normally expects a possessive suffix on the noun: minun äidinkieleni.

Correct options:

Äidinkieleni on ruotsi. ✔
Minun äidinkieleni on ruotsi. ✔ (more explicit/emphatic)

Wrong or unnatural:

Minun äidinkieli on ruotsi. ✖

The possessive suffix is the main marker of possession; the pronoun is optional for emphasis or clarity.

What exactly does äidinkieleni consist of? Why isn’t it just äidinkieli?

Äidinkieleni is built from three parts:

äidin = mother’s (äiti = mother, äidin = mother’s, genitive)
kieli = language / tongue
-ni = my (possessive suffix)

First, äidin + kieli → äidinkieli (mother’s language = mother tongue). That’s a compound noun. Then you add the possessive suffix -ni: äidinkieli + -ni → äidinkieleni (my mother tongue).

So äidinkieleni literally means my mother’s language-my, but in idiomatic English: my native language.

Why is the verb on and not olen? In English the subject is I, so why isn’t it I am?

In the Finnish sentence, the grammatical subject is äidinkieleni (my native language), not minä (I).

Äidinkieleni = it (3rd person singular)
The verb must match that, so it uses 3rd person singular: on = is

So the structure is literally: My native language is Swedish.
If you tried Minä olen ruotsi, that would mean I am Sweden / I am Swedish (the language), which is wrong here.

Why is ruotsi written with a small letter? In English Swedish is capitalized.

Finnish does not capitalize names of languages or nationalities. So you write:

ruotsi = Swedish (language)
englanti = English (language)
suomi = Finnish (language)

Country names, however, are capitalized:

Ruotsi = Sweden (country)
Englanti = England
Suomi = Finland

So Minun äidinkieleni on ruotsi. is correct with a lower-case r.

Can I change the word order, like Ruotsi on minun äidinkieleni or Äidinkieleni ruotsi on?

You can change the word order quite freely, but it affects emphasis:

Minun äidinkieleni on ruotsi.
Neutral: My native language is Swedish.
Äidinkieleni on ruotsi.
Very similar, slightly more compact.
Ruotsi on minun äidinkieleni.
Emphasis on ruotsi: It’s Swedish that is my native language (maybe in contrast to some other language).

Äidinkieleni ruotsi on is possible in some special contexts (poetry, very marked emphasis), but in normal speech/writing, stick to Äidinkieleni on ruotsi or Ruotsi on äidinkieleni.

Do I always need minun, or is Äidinkieleni on ruotsi enough?

Äidinkieleni on ruotsi is fully correct and usually preferred: the suffix -ni already shows that it’s my native language.

You add minun mainly for:

Emphasis: Minun äidinkieleni on ruotsi, ei suomi.
Contrast with someone else’s: Minun äidinkieleni on ruotsi, mutta hänen äidinkielensä on suomi.

So: minun is optional; the possessive suffix is the essential part.

How do I make this sentence negative? How do I say “My native language is not Swedish”?

Use the negative verb ei and change on to its basic form ole:

Minun äidinkieleni ei ole ruotsi. = My native language is not Swedish.
Or more compact: Äidinkieleni ei ole ruotsi.

Pattern:

Positive: X on Y.
Negative: X ei ole Y.

Why is there no word for a or the, like a native language or the native language?

Finnish has no articles like a/an or the. Definiteness and indefiniteness are usually understood from context and word forms.

In Minun äidinkieleni on ruotsi, the possessive suffix -ni already makes the phrase specific: my native language. There’s no need for the.

If you need to, you can clarify with extra words, but you never use a direct equivalent of English a or the.

Is äidinkieli always written as one word, or can I separate it?

It is written as one word: äidinkieli. In Finnish, many concepts that are two words in English become compound words:

äidin
- kieli → äidinkieli
kieli
- kurssi → kielikurssi (language course)

So you should not write äidin kieli here when you mean native language; that would emphasize the language of (my) mother more literally, not the fixed concept mother tongue.

How can I use this pattern with other languages and people? For example, “Her native language is English.”

You follow the same pattern but change the possessor and the language:

Hänen äidinkielensä on englanti. = Her/His native language is English.
- hän = he/she
- hänen = his/her (genitive)
- äidinkieli
  - -nsä → äidinkielensä (his/her native language)
- englanti = English (language)

More examples:

Äidinkieleni on suomi. = My native language is Finnish.
Äidinkielesi on saksa. = Your native language is German.
Heidän äidinkielensä on venäjä. = Their native language is Russian.