Til tross for at sykkellykten virker, er sykkelsetet og sykkelskjermen ødelagte.

It means even though, although, or more literally despite the fact that.

So:

• Til tross for at sykkellykten virker = Even though the bike light works

A useful pattern is:

• til tross for + noun phrase
  Til tross for regnet = Despite the rain
• til tross for at + clause
  Til tross for at det regner = Even though it is raining

Because til tross for by itself is followed by a noun or pronoun, not a full clause.

Compare:

• til tross for regnet = despite the rain
• til tross for dette = despite this

But if you want to follow it with a whole clause containing a verb, you normally use at:

• til tross for at sykkellykten virker

So at is what lets the expression introduce a full subordinate clause.

This is because Norwegian main clauses follow the V2 rule: the finite verb is usually in the second position.

The first position here is taken by the whole opening clause:

• Til tross for at sykkellykten virker

So in the main clause, the verb comes next:

• er sykkelsetet og sykkelskjermen ødelagte

If you put the subject first instead, you would get:

• Sykkelsetet og sykkelskjermen er ødelagte, til tross for at sykkellykten virker.

Both are grammatical; the original just fronts the contrast.

Because Norwegian very often makes compound nouns where English might use separate words.

So:

• sykkel + lykt = sykkellykt
• sykkel + sete = sykkelsete
• sykkel + skjerm = sykkelskjerm

Then the definite ending is added to the whole compound:

• sykkellykten = the bicycle light
• sykkelsetet = the bicycle seat
• sykkelskjermen = the bicycle fender/mudguard

A good rule for learners is: if English has a noun + noun combination, Norwegian often writes it as one word.

Yes, sykkellykta is also possible in Bokmål.

The noun lykt is feminine, but in Bokmål many feminine nouns can also be treated as common gender. That gives two possible definite singular forms:

• sykkellykta
• sykkellykten

Both are acceptable in Bokmål. Which one you see depends on style, region, and personal preference.

Here it means works or functions.

With a device or mechanism, virke often means:

• The light works
• The machine functions

So:

• sykkellykten virker = the bicycle light works

But virke can also mean seem in other contexts:

• Det virker vanskelig = It seems difficult

So the meaning depends on context.

Here sykkelskjermen means the bicycle fender or mudguard, not a screen.

The word skjerm can mean different things depending on context:

• screen
• shield
• fender/mudguard

In a bicycle sentence, sykkelskjerm normally means the part over the wheel that blocks water and dirt.

Because the subject is plural in meaning: it refers to two things joined by og:

• sykkelsetet og sykkelskjermen

When a predicative adjective describes more than one thing, it normally takes the plural form:

• er ødelagte = are broken

Compare:

• Sykkelsetet er ødelagt = The bike seat is broken
• Sykkelskjermen er ødelagt = The bike fender is broken
• Sykkelsetet og sykkelskjermen er ødelagte = The bike seat and the bike fender are broken

Because the sentence is talking about specific, identifiable parts.

The definite forms mean:

• sykkellykten = the bicycle light
• sykkelsetet = the bicycle seat
• sykkelskjermen = the bicycle fender

If the sentence were talking about these items in a general or indefinite way, you would use indefinite forms such as:

• en sykkellykt
• et sykkelsete
• en sykkelskjerm

In the original sentence, it sounds like we already know which bike and which parts are being talked about.

In normal learner-friendly Norwegian, repeating it is the safest choice.

• sykkelsetet og sykkelskjermen

If you said just skjermen, it could easily sound like the screen instead of the bicycle fender, unless the context is very clear.

Native speakers can sometimes avoid repetition in special ways, but for learners, repeating the compound is the clearest and most natural option.