Við höfum verið að bíða síðan í morgun.

Because the sentence describes an action that started earlier and is still continuing now.

• Við bíðum = We wait / We are waiting in a general or simple present sense.
• Við erum að bíða = We are waiting right now.
• Við höfum verið að bíða = We have been waiting.

So höfum verið að bíða is the best match for the English have been waiting.

In this pattern, vera að + infinitive is used to show that someone is in the middle of doing something.

So:

• vera að lesa = to be reading
• vera að borða = to be eating
• vera að bíða = to be waiting

When you put that into the perfect, you get:

• hafa verið að bíða = to have been waiting

So the að is part of a common verbal construction, not a separate word you would translate literally by itself here.

Höfum is the 1st person plural present form of hafa (to have).

The subject is við = we, so the verb must match it:

• ég hef = I have
• þú hefur = you have
• við höfum = we have

That is why the sentence begins with:

• Við höfum ... = We have ...

Verið is the past participle of vera (to be).

In the perfect construction with hafa, Icelandic uses the past participle:

• hef verið = have been
• hefur verið = has been
• höfum verið = have been

So:

• Við höfum verið að bíða literally follows the pattern we have been waiting.

Also, verið does not change here for gender or number in this construction.

Because the sentence contains the construction vera að + infinitive.

After að in this pattern, you use the infinitive:

• að bíða = to wait

So:

• höfum verið að bíða = have been waiting

If you used beðið, that would be the past participle of bíða, and it would belong to a different structure, for example:

• Við höfum beðið síðan í morgun.

That can also mean We have waited / We have been waiting since this morning, but höfum verið að bíða puts extra emphasis on the ongoing nature of the action.

Yes, it is possible.

There is a subtle difference:

• Við höfum beðið síðan í morgun = a more compact perfect form; often understood as We have been waiting since this morning
• Við höfum verið að bíða síðan í morgun = more explicitly emphasizes the ongoing activity

So both can work, but verið að bíða sounds more like the English progressive have been waiting.

It means since this morning.

• síðan = since
• í morgun = this morning

So together:

• síðan í morgun = since this morning

This tells you the starting point in time of the waiting.

Because í morgun is the normal Icelandic expression for this morning.

Similarly:

• í gær = yesterday
• í dag = today
• í morgun = this morning
• í kvöld = tonight / this evening

So in the sentence, síðan í morgun is the natural idiomatic way to say since this morning.

Not always. Síðan can mean different things depending on context.

Common meanings include:

• since
• then / afterwards

In this sentence, because it is followed by a time expression and refers to duration up to now, it means since:

• síðan í morgun = since this morning

This is the normal straightforward word order for a main clause in Icelandic:

• Subject: Við
• Finite verb: höfum
• then the rest of the verbal phrase: verið að bíða
• then the time expression: síðan í morgun

So the structure is very natural and ordinary.

A rough breakdown is:

• Við = we
• höfum = have
• verið að bíða = been waiting
• síðan í morgun = since this morning

Both patterns exist, but they mean slightly different things.

• bíða on its own = wait
• bíða einhvers can mean wait for something/someone in a more formal or older-style case-governed way
• bíða eftir einhverjum/einhverju is very common for wait for someone/something

In your sentence, there is no object, so plain bíða is enough:

• Við höfum verið að bíða ... = We have been waiting ...

If you wanted to say We have been waiting for the bus since this morning, you would very naturally say:

• Við höfum verið að bíða eftir strætó síðan í morgun.

You put ekki after the finite verb:

• Við höfum ekki verið að bíða síðan í morgun.

That means:

• We have not been waiting since this morning.

This is the usual placement of ekki in a main clause.

It is completely normal and natural Icelandic. The hafa verið að + infinitive pattern is especially common in everyday speech when speakers want to stress that an action has been ongoing.

So it does not sound strange at all. It is a very natural way to express have been waiting.