Learn Hardcore Finnish: Minä haluan tutustua Suomeen paremmin.

Yes. In Finnish the subject pronoun is usually omitted because the verb ending shows the person. So Haluan tutustua Suomeen paremmin is perfectly natural. Keeping Minä adds emphasis or contrast (e.g., “I want to, but others don’t”). In casual speech you’ll hear: Mä haluun tutustua Suomeen paremmin.

What does haluan tell me about person and tense? Are there polite/negative forms?

Haluan is 1st person singular present of haluta “to want”; the -n ending means “I”. Finnish has no separate future tense, so present can express future intention. For politeness, use the conditional: Haluaisin tutustua… (“I’d like to…”). Negation uses the negative verb: En halua tutustua… (“I don’t want to…”).

Why is it tutustua (the infinitive) and not tutustun?

After haluta you use the A-infinitive of the next verb: haluan tutustua = “I want to get to know.” Tutustun is a finite form meaning “I (am) get(ting) to know.” Both are correct in different contexts:

Haluan tutustua Suomeen. (I want to get to know Finland.)
Tutustun Suomeen. (I’m getting to know Finland.) After movement verbs, you’ll see the -maan/-mään form: Lähden tutustumaan Suomeen.

What case is Suomeen, and why that case with tutustua?

Suomeen is the illative singular (“into Finland”). Tutustua governs the illative: tutustua johonkin “to get acquainted with something/someone” (literally “into something”). Examples: tutustua sinuun (“get to know you”), tutustua uuteen kaupunkiin (“get to know a new city”).

Why not Suomea here?

Suomea is partitive. Some verbs require partitive (e.g., rakastaa Suomea “to love Finland”), but tutustua takes the illative complement. Therefore: tutustua Suomeen.

How is Suomeen formed from Suomi?

With many native i-stem nouns, the i changes to e before case endings. The illative singular lengthens the last vowel and adds -n:

Suomi → Suome- + en → Suomeen (the double e marks a long vowel). Similar patterns: järvi → järveen, ovi → oveen.

Could I use Suomessa or Suomesta instead?

Not with tutustua.

Suomessa = “in Finland” (inessive, location).
Suomesta = “from Finland” (elative, movement out of).
Suomeen = “to/into Finland” (illative, movement into or target of acquaintance). After tutustua, use the illative: tutustua Suomeen.

What does paremmin mean, and why not parempi?

Paremmin is the comparative adverb “better” (modifies verbs). Parempi is the comparative adjective “better” (modifies nouns). Here we modify the action tutustua, so we need paremmin. Irregular comparative of “well”: hyvin → paremmin → parhaiten.

Where can I place paremmin in the sentence?

All of these are acceptable; the first is most neutral:

Haluan tutustua Suomeen paremmin.
Haluan tutustua paremmin Suomeen.
Haluan paremmin tutustua Suomeen. (possible but a bit marked/formal) Keep the adverb near the verb it modifies.

Is enemmän (“more”) a good alternative to paremmin here?

Use paremmin for “better” (quality), not enemmän (quantity).

Quality: Haluan tutustua Suomeen paremmin. (get to know better)
Quantity: Haluan matkustaa Suomessa enemmän. (travel more)

Is there a more “thorough” or formal way to say this?

Yes:

Haluaisin perehtyä Suomeen paremmin. (to delve into, study in depth)
Haluan oppia tuntemaan Suomen paremmin. (learn to know Finland better; deeper knowledge)

Why is it Suomen after oppia tuntemaan, not Suomeen?

Oppia tuntemaan takes a direct object, so you use the total object form Suomen (genitive/accusative), not the illative. Tutustua instead takes an illative complement: Suomeen.

How would I say “I want to get to know Finns better”?

Haluan tutustua suomalaisiin paremmin. Note the plural illative -iin: suomalainen → suomalaisiin.

How do I negate the whole sentence?

Use the negative verb and the connegative main verb: En halua tutustua Suomeen paremmin. (“I don’t want to get to know Finland better.”)

Any difference between written and spoken Finnish here?

Colloquial speech often shortens forms:

Minä haluan → Mä haluun
Everything else stays similar: Mä haluun tutustua Suomeen paremmin. Written standard: (Minä) haluan tutustua Suomeen paremmin.

How do I pronounce the tricky parts?

haluan: ha-lu-an (3 syllables).
tutustua: tu-tus-tu-a (4 syllables; the u-a are separate).
Suomeen: suo-meen (diphthong uo, then long ee; hold the double vowel).

Can I say Suomiin?

That’s the plural illative (“into the Finlands”), which doesn’t make sense here. Use the singular illative Suomeen.