Pidän kaikesta paitsi kahvista.

Pidän is the 1st person singular form of the verb pitää when it means to like.

• dictionary form: pitää
• minä pidän = I like

Finnish usually drops the subject pronoun when it is clear from the verb ending, so pidän by itself already means I like.
That is why minä pidän and pidän can both mean the same thing, but pidän is the more natural neutral version in many contexts.

As for pitän: that form is just not how this verb changes. The stem changes slightly:

• pitää → pidän
• pidät
• pitää
• pidämme, etc.

This is a normal type of Finnish verb change.

Here pitää means to like.

That is important because pitää can also mean other things in other contexts, especially:

• must / have to
  
  • Minun pitää mennä. = I have to go.
• to hold / keep in some uses

In Pidän kaikesta paitsi kahvista, it clearly means to like.

Because the verb pitää in the meaning to like requires its object-like complement in the elative case: -sta / -stä.

So:

• pidän kahvista = I like coffee
• pidän musiikista = I like music
• pidän kaikesta = I like everything

The base word is kaikki = everything / all.
In this sentence it becomes kaikesta, which is the elative singular form.

So the structure is:

• pidän + elative

For the same reason: pitää meaning to like requires the thing liked to be in the elative.

So:

• Pidän kahvista. = I like coffee.

In your sentence, kahvista comes after paitsi, but it still stays in the form the sentence requires.

So the logic is basically:

• Pidän kaikesta.
• Pidän kahvista.

Therefore:

• Pidän kaikesta paitsi kahvista.

Yes. Paitsi means except / except for / but not.

In this sentence:

• kaikesta = everything
• paitsi kahvista = except coffee

So paitsi introduces the exception.

A useful point: the word after paitsi often appears in the case that fits the grammar of the whole sentence, as it does here.

Not exactly. The more important reason is that pitää requires the liked thing to be in the elative.

So kahvista is in elative because it is the thing being excepted from the set of things the speaker likes.

You can think of it like this:

• Pidän kaikesta.
• En pidä kahvista.

Combined:

• Pidän kaikesta paitsi kahvista.

So the case is really coming from the verb pattern, not simply from paitsi by itself.

Because with pitää meaning to like, Finnish normally uses the elative, not the partitive.

So these are correct:

• Pidän kahvista.
• Pidän kaikesta.

Not:

• Pidän kahvia.
• Pidän kaikkea.

A native English speaker often expects a direct object after like, but Finnish does not work that way with this verb.
It is one of those verbs whose complement uses a specific case.

The basic form is kaikki.

Here are the useful forms:

• kaikki = all / everything
• kaikesta = from everything / about everything / in this pattern, everything after pitää

In this sentence, kaikesta is best understood as everything, but grammatically it is in the elative form.

It is singular.

That may feel surprising, because English everything sounds semantically broad, almost like a plural idea. But in Finnish:

• kaikki can mean everything as a singular totality
• kaikesta is the singular elative form of that word

So even though it refers to all things in general, the form here is singular.

Yes, absolutely.

• Pidän kaikesta paitsi kahvista.
• Minä pidän kaikesta paitsi kahvista.

Both are grammatical.

Adding minä makes the subject more explicit. It may sound:

• more emphatic
• contrastive
• or just slightly more explicit in context

But in neutral everyday Finnish, leaving out minä is very common.

Pidän kaikesta paitsi kahvista is the normal and natural order.

Finnish word order is fairly flexible, but this version is the clearest default:

• Pidän = I like
• kaikesta = everything
• paitsi kahvista = except coffee

You might move things around in special contexts for emphasis, but for a learner this is the best order to use.

Yes, that is a very natural way to understand it.

Depending on context, kaikesta can sound broad and general:

• I like everything
• I like all sorts of things
• I like everything except coffee

The exact English wording may vary a little, but the Finnish grammar stays the same.

A simple negative sentence would be:

• En pidä kahvista. = I don’t like coffee.

That shows the same verb pattern clearly:

• pidän kahvista = I like coffee
• en pidä kahvista = I don’t like coffee

Notice that in the negative:

• pidän changes to pidä
• kahvista stays in the same case

That is useful because your sentence is really built around the same pattern.

The biggest takeaway is:

pitää = to like takes the elative case (-sta / -stä) for the thing liked.

So memorize examples like these:

• Pidän kahvista. = I like coffee.
• Pidän musiikista. = I like music.
• Pidän kaikesta. = I like everything.
• Pidän kaikesta paitsi kahvista. = I like everything except coffee.

If you remember that pattern, this whole sentence becomes much easier to understand.