Við vitum ekki hvort báturinn fer á réttum tíma, en við ætlum samt að bíða við bryggjuna.

Hvort introduces an indirect yes/no question, so here it means whether.

• Við vitum ekki hvort ... = We do not know whether ...
• It is different from a direct question:
  • Fer báturinn á réttum tíma? = Does the boat leave on time?
• In the sentence you gave, that question is embedded inside a larger statement, so Icelandic uses hvort.

English often uses if in this kind of sentence, but hvort is the standard Icelandic word for whether in this structure.

Báturinn means the boat. The ending -inn is the suffixed definite article in Icelandic.

• bátur = a boat / boat
• báturinn = the boat

This is very common in Icelandic: instead of putting a separate word like English the, Icelandic often adds the article to the noun itself.

Here, báturinn is in the nominative singular because it is the subject of fer.

Fara is the infinitive, meaning to go / to leave / to travel.
Fer is the 3rd person singular present tense form.

So:

• að fara = to go
• ég fer = I go
• þú ferð = you go
• hann / hún / það fer = he / she / it goes
• báturinn fer = the boat goes / leaves

Since báturinn is singular, the verb must also be singular: fer.

Because this is a subordinate clause, not a main question.

In a main question, Icelandic often has verb-first order:

• Fer báturinn á réttum tíma? = Does the boat leave on time?

But after hvort, the clause becomes embedded, and the normal subordinate-clause order is used:

• hvort báturinn fer á réttum tíma

So the subject báturinn comes before the verb fer.

Because á here takes the dative in this time expression, and the adjective has to match the noun.

The base phrase is:

• réttur tími = the correct/right time

But after á in this usage, it becomes dative:

• á réttum tíma = at the right time / on time

The forms are:

• réttur → nominative masculine singular
• réttum → dative masculine singular
• tími → nominative
• tíma → dative

So both the adjective and noun change form to show case.

Literally, it is at the right time, but in natural English it often corresponds to on time.

So in this sentence, it means that the boat leaves at the scheduled or proper time, not late.

This is a good example of how Icelandic and English may use slightly different wording even when the meaning is the same.

Because að bíða is an infinitive phrase, and after ætla Icelandic normally uses að + infinitive.

• ætla = to intend / to plan / to be going to
• við ætlum að bíða = we intend to wait / we are going to wait

So:

• við ætlum = we intend
• að bíða = to wait

This is a very common pattern:

• Ég ætla að fara. = I’m going to go.
• Við ætlum að bíða. = We’re going to wait.

Ætlum is the 1st person plural present tense of ætla.

• ég ætla = I intend / I am going to
• við ætlum = we intend / we are going to

In this sentence, it expresses intention or plan:

• við ætlum samt að bíða = we still plan to wait / we are going to wait anyway

Depending on context, ætla can sound like:

• intention: intend to
• plan: plan to
• near future: be going to

Samt means still, anyway, or all the same, depending on context.

Here it shows contrast:

• We don’t know whether the boat leaves on time, but we’re going to wait anyway.

Its position is natural in Icelandic after the finite verb phrase:

• við ætlum samt að bíða

That placement is very common. It gives the sense of nevertheless / even so.

Bryggjuna is accusative singular with the definite article, so við bryggjuna means by the pier / at the pier.

The noun is:

• bryggja = pier / dock
• bryggjan = the pier (nominative)
• bryggjuna = accusative definite form

The preposition við often takes the accusative. In this sentence it means by / at / next to.

So:

• við bryggjuna = by the pier

Even though there is no movement toward the pier in English, Icelandic still uses við with accusative here.

They are spelled the same, but they are different words.

• Við at the start = the pronoun we
• við before bryggjuna = the preposition by / at / next to

So in the same sentence you have:

• Við vitum ekki ... = We do not know ...
• við bryggjuna = by the pier

This is very normal in Icelandic, and context tells you which one it is.

Yes, bíða can take an object when you say what you are waiting for.

For example:

• bíða bátsins = wait for the boat
  traditionally, bíða takes the genitive when it has this kind of object

But in your sentence, the focus is only on the location:

• að bíða við bryggjuna = to wait by the pier

The sentence does not explicitly say what they are waiting for, even though it is easy to infer it from context.

It has two main parts joined by en = but.

1. Við vitum ekki hvort báturinn fer á réttum tíma

   • main clause: Við vitum ekki = We do not know
   • subordinate clause: hvort báturinn fer á réttum tíma = whether the boat leaves on time

2. en við ætlum samt að bíða við bryggjuna

   • en = but
   • við ætlum = we intend / we are going to
   • samt = anyway / still
   • að bíða við bryggjuna = to wait by the pier

So the whole sentence is basically:

• uncertainty in the first half
• determination in the second half

A learner would probably want to remember these:

• vita = to know
  • við vitum = we know
• fara = to go / leave
  • fer = goes / leaves
• ætla = to intend / be going to
  • við ætlum = we intend / we are going to
• bíða = to wait

So this one sentence gives you several very useful patterns:

• við vitum ekki hvort ...
• X fer á réttum tíma
• við ætlum að ...
• bíða við ...