Matka tuntuu helpolta, kun juna on nopea.

Because the grammatical subject is matka (the trip/journey), which is singular. The verb tuntua (to feel/seem) agrees with its subject in person/number, so matka tuntuu = the trip feels/seems.

Matka is the subject. In Finnish, the thing that “feels” a certain way is commonly the subject with tuntua:

• Matka tuntuu… = The trip feels…
  There isn’t a direct object in this sentence.

Helpolta is the adjective helppo in the ablative case (-lta/-ltä). This is a standard construction with tuntua:

• tuntua joltakin = to feel/seem like something

So tuntuu helpolta literally follows the pattern feels (like) easy.

Finnish doesn’t normally use a plain nominative adjective as the complement of tuntua. With olla you’d use nominative:

• Matka on helppo. = The trip is easy. (more objective statement)

With tuntua, Finnish typically uses the joltakin pattern:

• Matka tuntuu helpolta. = The trip feels easy. (speaker’s impression)

Usually helpolta is the natural choice for “feels/seems easy.”
Helpoksi (translative -ksi) can exist, but it more easily suggests “seems/turns out (to be) easy” in a classificatory or result-like sense, depending on context. For a straightforward “feels easy,” helpolta is the safe default.

Kun can mean both, depending on context. Here it can be understood as:

• when / as: the trip feels easy when the train is fast (general condition)
• because: the trip feels easy because the train is fast (reason)

If you want an unambiguously causal “because,” koska is often used:

• …koska juna on nopea.

Finnish normally uses a comma before a subordinate clause introduced by kun, koska, että, etc. So:

• Matka tuntuu helpolta, kun …
  is standard punctuation.

Because on is the verb olla (to be), which links the subject to a predicate adjective:

• juna on nopea = the train is fast (adjective describing the train)

An adverb would describe an action, e.g.:

• Juna kulkee nopeasti. = The train moves fast.

In an affirmative copula sentence like this, the predicate adjective is typically nominative:

• Juna on nopea.

Partitive (nopeaa) would appear in contexts like negation or certain “partial/indefinite” meanings:

• Juna ei ole nopea. (often nominative in modern Finnish)
• Juna ei ole nopea/nopeaa. (variation exists; usage depends on dialect/style and nuance)

For a basic positive statement, nopea is the expected form.

Present tense (on) makes it a general statement or present-time condition:

• …kun juna on nopea. = …when/because the train is fast.

Past tense (oli) would shift the condition to the past:

• Matka tuntui helpolta, kun juna oli nopea. = The trip felt easy when/because the train was fast.

No. Finnish has no articles (the / a). Context supplies definiteness:

• Matka can be a trip or the trip
• juna can be a train or the train

The meaning stays mostly the same, but focus changes. You can front the clause:

• Kun juna on nopea, matka tuntuu helpolta.
  This puts the condition/reason first, which can sound slightly more explanatory or structured.