The setting seems very important to the story, so I’d like to see/hear/smell, etc., more uniquely Icelandic details. Make the setting so strong that it’s almost a character.

I also noticed that people’s names are mentioned but who they actually are isn’t explained until several paragraphs later. This is distracting and can also make figuring out the different relationships between the characters somewhat confusing.

While I realize that this is probably a first draft, it is badly in need of being proofread. Also, it would be immensely helpful for you to invest in a good book on grammar. Commas are either misused or not used at all, and plurals, possessives, and contractions are often mixed up (“its” vs. “it’s”; “eye’s” vs. “eyes”). Words often seem to be misused as well. It’s impossible to be a good author without having a good grasp on the basic elements of language.

More specific comments:
Why present tense? I find it somewhat distracting.

Switching back and forth between Helen and Ben makes it choppy reading. I think I understand the effect you’re going for – portraying the simultaneity of events – but the timing seems somewhat off, and the mundanity of what Ben is doing makes it even more questionable. I found myself wanting to read more about Helen because she’s doing something exciting. The contrast between the two is interesting…but not interesting enough to make me want to read about Ben and his work.

I think Helen’s name needs to be given in the first paragraph. When it finally shows up in the third paragraph, it takes the reader a second to connect the “She” in the first paragraph to Helen.

“Taking a water bottle from a side pocket she pulls free a stopper and puts the neck to her lips and quenches her thirst with cold, fresh, mountain water.” — This sentence has a bit of a dangling participle. Not quite, exactly, but it does seem to be saying that she’s pulling out the stopper, putting the bottle to her lips, and quenching her thirst as she taking the bottle out of her side pocket. The sentence itself is somewhat awkward, possibly because of the elements of the sentence being linked with “and” twice. It has a running-on quality without being a true run-on.

“She manages a last enthusiastic grin to Andy.” — Who is Andy? Give him a little description or explanation, the way you did when you introduced Finnur.

“Sitting up sharply in bed, Ben breathes fast, “Helen—” he allows himself to say. Visions and echoes of his dream flash fast through his mind.” — At this point, I’m very confused. Was all the stuff with Helen and Ben with his computer Ben’s dream? Or is the dream the next paragraph? This is where the timing gets off for me too. Ben is working on his computer at night, while Helen is hiking. Is Helen hiking at night? Is it an Icelandic night, so there is still enough light to see by?

“A cacophony of noise echoes down the emotionless halls.” — “emotionless” doesn’t work for me here. Halls are always emotionless.

“A voice. His head turns. The wild, fair hair of his father. He’s been crying.” — Ben’s father has been crying? His father’s hair has been crying? Ben has been crying? It’s unclear.

“And Ben’s sister – Helen – lying motionless against a rock.” — In the hallway? I’m assuming this is a dream, but it’s still very confusing. Dreams are often confusing, it’s true, but they can be written in such a way that illustrates their confusion while still being clear for the reader. The relationship between Ben and Helen should be explained earlier on. It might make the switching between them slightly less puzzling.

“Unplugging them from the armrest he wraps the lead up round the ear pieces.” — I’m not really sure if the reader needs all these details. They don’t seem relevant at all.

“Beyond, through the glass, a jet’s nose piece hatches from a vast cylindrical metal egg poised on tons of grey rock.” — This is a bizarre image. What is it describing?

“The inevitability of the situation argues with his mind, scientific fact and probability throwing out human optimism.” — This sentence is very awkward, even though I understand what is being said. The part that sticks out to me is “The inevitability of the situation argues with his mind”, “his mind” in particular. Maybe “his heart” would be better? Or “is at odds with” instead of “argues”?

“The room sinks into Icelandic summer darkness – a washed-out colourless light.” — I like this description very much. When you describe things that are unique to Iceland and its landscape, it’s very interesting.

“An hour later, he turns in the bed, tugging at the covers, desperately counting sheep, willing himself to sleep.” — Cut “willing himself to sleep”, since it’s already covered by “desperately counting sheep”.

“Exactly,” Hanna confronts her cousin.” — I’m not sure if “confronts” is the right word here.

During this scene with Hanna and Ben, I understand that you are trying portray the feelings of helplessness of relatives in this situation, but the step-by-step recounting of so many mundane details and actions is becoming somewhat plodding and dull. I find myself skimming instead of reading. I want something to happen!

“He’s there again in an instant, sitting across the table from, and laughing and joking with, his sister. Helen.” — The comma after “with” shouldn’t be there. Be careful with commas in general. They’ve been misused or not used at all a lot so far.

“What is he going till to then, she asks.” — This is awkward and there appears to be a word missing. Maybe you should just make it regular dialogue.

“This whole event has destroyed him.” — It’s cliché writing advice, but show, don’t tell. The reader can get that feeling of distress without being told directly.

“He scratches it from the page, with the ball of his pen.” — “…with the ball of his pen” is unnecessary and stiff.

“He stares at them. He turns and looks at the photograph of Gulfoss.” — Establish the name of the waterfall in the photo the first time you mention it.

“He sees her – there – over the far side of the platform, next to the telephone kiosks and stairs. He lifts his hand to wave. She’s seen him.” — Is this a flashback? A dream? A hallucination? I think that Ben has been knocked unconscious, but it’s not clear enough. Also, there should probably be a space break before this part, rather than just a simple paragraph break.

“Now, she has graduated – although how well she will have to wait a few months longer to find out…” — This is awkward.

“He’s ashen faced and tired looking, stretched.” — He looks stretched?

“Their sibling eyes cross the yard.” — This is an awkward and ineffective sentence and description. Maybe “The siblings’ eyes meet from across the yard.”?

“They could be the times of a the local bus service, accept even that would have some meaning.” — Delete “a” before “the”, and replace “accept” with “except”.

“Helen soon joins the reunion, each speaking their feelings in an unstructured orchestration of sound.” — Should that be “Heather”? I’m not sure who Heather is yet, maybe explain it when you first mention her name? Also, “unstructured orchestration of sound” is needlessly wordy. Anglo-Saxon-based words are more immediate than Latinate words and tend to sound less pretentious and wordy.

“Oddly it is Guðni and Heather who find humour the greatest relief, with Baldur and Eyrún joining in reluctantly and with hard felt guilt.” — I’m feeling confused about the relationships here. Who is Baldur? Who are Ben and Helen’s parents?

‘“How can you be so sure?” Eyrún rallies on her brother,’ — I don’t think “rallies” is the right verb to use here.

‘“You don’t know what it’s been like this year?”’ — This isn’t a question.

“Guðni embraces his sister, telling her it’s not so. It’s just coincidence, that you are only noticing these things now…” — The second person pronoun doesn’t work in this sentence.

“She reacts violently towards his words…” — Show, don’t tell.

“The cloud has broken in a swathe across the horizon, and a sunset is rich in gold, red, mauve and orange.” — This is very nice.

“Ben lays in the temperature rich water of the tub.” — This is a pointlessly complex way of saying “hot.”

“Waves washe (sic) over his face, and the level is displaced.” — What level? The water level? Again, it’s a rather stiff and complex way of describing something that’s actually very simple.

“Pencil, hovering over paper, his research is set out in front of him.” — “Pencil hovering over paper” is a dangling participle. Right now, the sentence is saying that the pencil’s research is set out in front of him.

“Almost by it’s own will…” — “its” is possessive; “it’s” is a contraction.

“His pencil moves fast, putting down onto the page the detail, and the method of his discovery.” — What is Ben studying? It seems to have something to do with weather patterns, but it’s never made explicit.

“An Italian tourist stops outside a bar on Reykjavik high street and begins reading through the menu taped to the inside of the glass.” — Why are we focusing on a random Italian tourist? We don’t get any special insight from looking through this person’s eyes. Maybe you should limit the number of people whose point of view is seen.

“Pausing, her teeth suck on her bottom lip, in thought.” — This sentence needs to be rewritten. At the moment, it’s saying that her teeth are pausing.

“A line of words grow across the page and return.” — This should be “A line of words grows across the page…” because “line” is singular. Or it could be “Lines of words grow…”

“Ben sits back in his chair, breathing out with relief he cast down his pencil onto the paper.” — This sentence is very awkward and needs to be rewritten.

“Hanna questions his intentions although unsurprised by his actions…” — Show, don’t tell. We can tell from the dialogue that she’s questioning his intentions.