Learn Hardcore Finnish: Minusta tämä paikka on kaunis. - In my opinion, this place is beautiful.

Literally, Minusta tämä paikka on kaunis is something like From me, this place is beautiful, which in natural English becomes I think this place is beautiful / In my opinion, this place is beautiful.

In this construction:

minusta does not act as the grammatical subject.
It marks the experiencer / source of the opinion.
The true subject is tämä paikka (this place).

So the pattern is:

minusta / sinusta / hänestä / meistä / teistä / heistä
- [clause]
= In my / your / his-her / our / your / their opinion, [clause].

Why is it Minusta and not Minä? Could I say Minä tämä paikka on kaunis?

You cannot say Minä tämä paikka on kaunis; that is ungrammatical.

In Finnish, the idea I think / I find / In my opinion is not normally expressed by just putting minä (nominative) in front of a clause without a verb. Instead:

If you use this opinion construction, you must use the elative form:
- Minusta tämä paikka on kaunis.
If you want to use minä as a normal subject, you also need a verb like:
- Minä luulen, että tämä paikka on kaunis.
  (I think / I suppose that this place is beautiful.)
- Minä ajattelen, että…, Minä uskon, että…, etc.

So:

Minä alone in front of a sentence does not mean I think.
The structure Minusta … on kaunis is a specific pattern: [experiencer in elative] + [something] + on + [adjective] ≈ I find [something] [adjective].

Is Minusta required? What is the difference between Tämä paikka on kaunis and Minusta tämä paikka on kaunis?

Both are correct, but they feel different:

Tämä paikka on kaunis.
- A plain statement: This place is beautiful.
- Sounds more like an objective fact or a neutral description.
Minusta tämä paikka on kaunis.
- Explicitly marks it as your personal opinion / feeling.
- Similar to I think this place is beautiful or To me, this place is beautiful.
- Can sound a bit softer or more subjective, as if you are saying at least in my view.

So:

Is Minusta necessary?
No. The sentence is grammatically fine without it.
Why use it?
To signal clearly that this is your subjective evaluation, not a universal fact you are stating.

Can the word order change? Are Minusta tämä paikka on kaunis, Tämä paikka on minusta kaunis, and Tämä paikka on kaunis minusta all correct, and do they mean the same?

All three are grammatically correct and convey essentially the same basic meaning, but the focus and tone change slightly.

Minusta tämä paikka on kaunis.
- Very common and natural.
- Focus on your viewpoint:
  As for me / In my opinion, this place is beautiful.
Tämä paikka on minusta kaunis.
- Also natural.
- Focus first on this place; then minusta specifies whose evaluation it is.
- Roughly: This place is, in my opinion, beautiful.
Tämä paikka on kaunis minusta.
- Less common in careful written language, but you hear it in speech.
- Minusta at the end can feel a bit like an afterthought:
  - This place is beautiful, to me.
- Still correct; just slightly different rhythm / emphasis.

In Finnish, word order is flexible, but the item placed earlier in the sentence tends to get more emphasis or topical focus. Here, the meaning stays the same, only the nuance changes.

What is the difference between Minusta tämä paikka on kaunis and Minun mielestäni tämä paikka on kaunis (or Mielestäni tämä paikka on kaunis)?

All of these mean essentially In my opinion this place is beautiful, but with small differences in style and structure.

Minusta tämä paikka on kaunis.
- Very common, short, and natural in both speech and writing.
- Slightly more informal / neutral.
Minun mielestäni tämä paikka on kaunis.
- Literally: From my mind, this place is beautiful.
  - minun = my (genitive)
  - mielestäni = from my mind (mieli + -stä + -ni)
- Sounds a bit more explicit and can be slightly more formal or careful.
- Often used when you want to stress that this is clearly just your personal view.
Mielestäni tämä paikka on kaunis.
- Same as minun mielestäni, but the minun is dropped and its role is carried by -ni (my) on mielestäni.
- Very common, perhaps a bit more neutral/formal than plain minusta.

Colloquial variants you will hear:

Mun mielestä tämä paikka on kaunis.
Musta tämä paikka on kaunis. (= Minusta tämä paikka on kaunis)

For a learner, you can treat:

Minusta…
Mielestäni… / Minun mielestäni…

all as natural ways to say In my opinion…. The nuance differences are minor.

How is this different from saying Minä luulen, että tämä paikka on kaunis or Minä ajattelen, että tämä paikka on kaunis? Which is more natural?

These sentences are grammatically fine, but they are not used in exactly the same way.

Minusta tämä paikka on kaunis.
- Neutral, very natural for expressing a value judgement / aesthetic opinion.
- Translates best as I think this place is beautiful or I find this place beautiful.
Minä luulen, että tämä paikka on kaunis.
- luulla ≈ to believe, to suppose, to think (with some uncertainty).
- Often used for guesses or beliefs about facts, e.g.:
  - Minä luulen, että hän on kotona.
    (I think / I suppose he is at home.)
- With adjectives like kaunis, this can sound like you are uncertain or you are reasoning about it:
  I guess this place is beautiful (maybe compared to something else).
Minä ajattelen, että tämä paikka on kaunis.
- ajatella = to think (in the sense of mental activity).
- Focuses on the thinking process, not so much on the evaluation itself.
- Can sound a bit heavy or deliberate in everyday speech.

For simple personal opinions about qualities (beautiful, ugly, nice, boring, interesting, etc.), the most natural everyday patterns are:

Minusta tämä paikka on kaunis.
Mielestäni tämä paikka on kaunis.

Use luulen, että… more for factual guesses:

Luulen, että bussi tulee pian.
(I think the bus will come soon.)

What case is paikka in, and why is kaunis in its basic form?

In Minusta tämä paikka on kaunis:

tämä paikka is the subject.
- tämä = this (demonstrative pronoun, nominative)
- paikka = place (noun, nominative singular)

So paikka is in the nominative singular, the normal subject form.

kaunis is an adjective functioning as a predicative (a description linked to the subject via on):

The verb olla (to be) connects the subject and its complement:
- Tämä paikka – on – kaunis.
In this basic pattern, the adjective is also in nominative and agrees in number with the subject.
For a singular subject like tämä paikka, the nominative singular of kaunis is simply kaunis, the same as the dictionary form.

Examples with number change:

Tämä paikka on kaunis.
This place is beautiful.
Nämä paikat ovat kauniita.
These places are beautiful.
(Here paikat = nominative plural; kauniita = partitive plural, which is very common for plural predicatives.)

For now, the key point is:

After on with a singular subject, an adjective like kaunis usually appears in its basic dictionary form, which here is already the correct form.

How do you negate this sentence?

To say In my opinion, this place is not beautiful, use the Finnish negative verb ei plus olla in the negative form ole:

Minusta tämä paikka ei ole kaunis.
In my opinion, this place is not beautiful.

Structure:

Minusta – in my opinion
tämä paikka – this place (subject)
ei – negative verb (3rd person singular)
ole – negative form of on
kaunis – beautiful (unchanged)

You can also leave out Minusta if the context already makes your viewpoint clear:

Tämä paikka ei ole kaunis.
This place is not beautiful.

Or you can replace kaunis with another adjective to express a stronger opinion:

Minusta tämä paikka on ruma.
In my opinion, this place is ugly.

How do I say the same kind of sentence with other persons (your opinion, his/her opinion, our opinion, etc.)?

You change minusta according to the person. The pattern is:

minä → minusta
sinä → sinusta
hän → hänestä
me → meistä
te → teistä
he → heistä

Examples:

Sinusta tämä paikka on kaunis.
You think this place is beautiful. / In your opinion, this place is beautiful.
Hänestä tämä paikka on kaunis.
He/She thinks this place is beautiful.
Meistä tämä paikka on kaunis.
We think this place is beautiful.
Teistä tämä paikka on kaunis.
You (plural) think this place is beautiful.
Heistä tämä paikka on kaunis.
They think this place is beautiful.

In colloquial speech you will also often hear:

musta = minusta
susta = sinusta

for example:

Musta tämä paikka on kaunis.
(Very common spoken Finnish.)

Does minusta always express an opinion, or can it mean other things?

Minusta is the elative form of minä, so in principle it means from me / out of me / about me. That can show up in several patterns:

Opinion / evaluation (the pattern in your sentence)
- Minusta tämä paikka on kaunis.
  In my opinion, this place is beautiful.
Feelings / experiences
- Minusta tuntuu, että tämä on vaikeaa.
  I feel that this is difficult.
- Minusta on kiva, että tulit.
  I find it nice that you came.
Becoming / origin
Here minusta can mean from me / out of me (as a starting point):
- Minusta tulee opettaja.
  I will become a teacher.
  (Literally: From me will come a teacher.)
- Minusta kasvoi vahva ihminen.
  I grew into a strong person.
More literal spatial / abstract uses (less common in beginner material)
- Ota se pois minusta.
  Take it away from me. (physically or metaphorically)
- Älä puhu pahaa minusta.
  Do not speak badly about me.

In everyday conversation, when minusta appears at the beginning of a sentence followed by an adjective or a clause, learners can usually interpret it as:

In my opinion / I feel that / I find that…

So it does not always express opinion, but in the specific pattern Minusta + [something] on [adjective], it very typically does.