Ný vinna er bæði áskorun og reynsla.

Icelandic has no separate indefinite article (a / an).

• ný vinna can mean a new job or new work, depending on context.
• If you want to make it definite (the new job), Icelandic adds a suffix to the noun and uses the weak form of the adjective:
  
  • nýja vinnan = the new job (literally: new-the job-the).

Because vinna is a feminine noun in the nominative singular, and the adjective must agree with it:

• Adjective nýr (new) in nominative singular:
  
  • masculine: nýr (e.g. nýr bíll – new car)
  • feminine: ný (e.g. ný bók – new book)
  • neuter: nýtt (e.g. nýtt hús – new house)

Since vinna is feminine: ný + vinna → ný vinna.

Ný vinna is the subject of the sentence: Ný vinna er bæði áskorun og reynsla.

• Case: nominative (the default case for subjects)
• Number: singular
• Gender: feminine (because of vinna)

So grammatically it’s [feminine nominative singular].

Yes, and it changes the meaning slightly:

• Ný vinna er bæði áskorun og reynsla.

  • General statement: A new job is both a challenge and an experience (speaking in general).

• Nýja vinnan er bæði áskorun og reynsla.

  • Specific statement: The new job is both a challenge and an experience (a particular job that speaker and listener know about).

Grammar in the second sentence:

• nýja = weak definite form of nýr (because the noun is definite)
• vinnan = vinna
  • the suffixed definite article -n.

Here, áskorun and reynsla are used in a general, abstract sense:

• áskorun = challenge (as a type of thing)
• reynsla = experience (as a general quality)

So they appear indefinite, with no definite suffix.

You could say:

• …er bæði áskorunin og reynslan.
  That would sound like you are talking about a particular challenge and the particular experience associated with this job. It’s possible, but more specific and less general.

In the given sentence, the speaker is making a broad, general statement, so the indefinite forms are natural.

They are in the nominative singular.

Reason: with the verb vera (to be), nouns that describe or identify the subject (predicate nouns) are normally in the same case as the subject, which is nominative.

• Subject: ný vinna – nominative
• Predicate nouns: áskorun, reynsla – nominative

So: Ný vinna (nom.) er bæði áskorun (nom.) og reynsla (nom.).

bæði … og means both … and.

Structure:

• bæði stands before the first item.
• og stands before the second item.

In this sentence:

• bæði áskorun og reynsla
  = both a challenge and an experience

It can link nouns, adjectives, verbs, whole phrases, etc.:

• Hann er bæði klár og duglegur.
  He is both smart and hard‑working.

Word order is similar to English both X and Y.

er is the present tense, singular form of vera (to be), used with ég / hann / hún / það (I / he / she / it) and also for singular subjects like ný vinna.

Present tense of vera:

• ég er – I am
• þú ert – you are (singular)
• hann / hún / það er – he / she / it is
• við erum – we are
• þið eruð – you are (plural)
• þeir / þær / þau eru – they are

So with ný vinna (singular), you correctly use er.

Icelandic reynsla is usually treated as an uncountable / mass noun, like experience in English when used in a general sense:

• Hún hefur mikla reynslu.
  She has a lot of experience.

In this sentence, reynsla means experience in general that you gain, not one particular event. Therefore it stays singular with no article:

• …er bæði áskorun og reynsla.
  = …is both a challenge and (a source of) experience.

vinna (noun, feminine)

• Basic meaning: work, job, employment
• Singular:
  
  • nom: vinna
  • acc: vinnu
  • dat: vinnu
  • gen: vinnu
• Plural:
  
  • nom: vinnur
  • acc: vinnur
  • dat: vinnum
  • gen: vinna

að vinna is also a very common verb meaning to work or to win.

áskorun (noun, feminine)

• Meaning: challenge (something difficult that tests you)
• Singular:
  
  • nom: áskorun
  • acc: áskorun
  • dat: áskorun
  • gen: áskorunar
• Plural (common form):
  
  • nom: áskoranir
  • acc: áskoranir
  • dat: áskorunum
  • gen: áskorana

reynsla (noun, feminine, usually uncountable)

• Meaning: experience (knowledge or skill gained by doing things)
• Singular:
  
  • nom: reynsla
  • acc: reynslu
  • dat: reynslu
  • gen: reynslu
• Plural forms exist but are rare and usually refer to distinct kinds of experiences; everyday use is mostly singular.

Approximate pronunciation (English-friendly):

• Ný – like nee (long ee)
• vinna – VIN-na (short i like in hit, double n held a bit longer)
• er – like air but shorter
• bæði – BYE-thi (ð like soft th in this, final i like i in bit)
• áskorun – OWS-ko-run (first syllable like ow in cow, r rolled)
• og – roughly og/ok, often with a soft g
• reynsla – RAYNS-la (ey like ay in day, ns clearly pronounced)

In IPA (one possible transcription):

/niː ˈvɪnːa ɛr ˈpaiːðɪ ˈausˌkɔːrʏn ɔɣ ˈreiːnsla/

Primary stress is always on the first syllable of each word in Icelandic.