Ég hef ekki áhyggjur, því að kennarinn hjálpar.

Icelandic expresses “to be worried” with the idiom hafa áhyggjur (“to have worries”), not with the verb vera (“to be”). So you say Ég hef áhyggjur (I’m worried), never Ég er áhyggjur. If you want to use an adjective with vera, you can say:

• Ég er áhyggjufullur (male) / Ég er áhyggjufull (female) = I’m worried/anxious.

Áhyggjur is practically a plural-only noun (pluralia tantum). You almost always see it in the plural to mean “worries/concerns.” That’s why modifiers also go in feminine plural:

• miklar áhyggjur (a lot of worries)
• engar áhyggjur (no worries)

Use the preposition af with the dative:

• Ég hef áhyggjur af prófinu. (I’m worried about the exam.)
• Hún hefur áhyggjur af heilsu hans. (She’s worried about his health.)
• Við höfum áhyggjur af veðrinu. (We’re worried about the weather.)

All can introduce a reason, but there are nuances:

• því að = “because.” Common in writing; neutral to slightly formal.
• af því að = “because.” Extremely common in speech; fully standard.
• þar sem = “since/as,” often when the reason is background/known.
• vegna þess að = “because/due to the fact that,” heavier/formal. Important: því by itself usually means “therefore,” not “because,” so keep the að.

After a subordinator like því að / af því að, use normal subordinate-clause order: subject before the finite verb. So:

• Correct: því að kennarinn hjálpar
• Not standard: því að hjálpar kennarinn
  (Inversion is for main clauses; subordinate clauses don’t do V2 in Icelandic.)

Often, yes. Hjálpa typically takes a dative person:

• Kennarinn hjálpar mér. (The teacher helps me.) To add what you’re being helped with:
• hjálpa mér með verkefnið (with the assignment)
• hjálpa mér við verkefnið (at/with the assignment)
• hjálpa mér að læra (to study/learn)

Yes, it’s grammatical, though leading with a reason is less common in very casual speech. For example:

• Af því að kennarinn hjálpar, hef ég ekki áhyggjur.
• Þar sem kennarinn hjálpar, hef ég ekki áhyggjur.
  Keep the comma after the clause.

Yes:

• Ég er ekki stressaður/stressuð. (I’m not stressed.)
• Ég er rólegur/róleg. (I’m calm.)
• Ég er áhyggjulaus/áhyggjulaus. (I’m worry-free.)
  Choose endings that match your gender.

Approximate guide:

• Ég ≈ “yeh” (often with a soft g-sound; many say it very quickly)
• því ≈ “THVEE” (voiceless th as in “thing”)
• að ≈ “ath” with a soft voiced th (as in “this”), very short
• hjálpar ≈ “HYAU-l-par” (the hj is like a breathy h + y; á like “ow” in “cow”)
• áhyggjur ≈ “OW-hig-yur” (stress on the first syllable)
• kennarinn ≈ “KEN-na-rin” (r is tapped/trilled)