אסור להם לנסוע על אופניים בלי קסדה.

Here אסור means forbidden / not allowed.

A very common Hebrew pattern is:

אסור ל־... + infinitive

So:

אסור להם לנסוע = It is forbidden for them to ride / They are not allowed to ride

Literally, it is closer to forbidden to them to ride than to the English wording.

Also, אסור is grammatically an adjective, but in this kind of impersonal expression it often stays in the default masculine singular form.

Because Hebrew uses the pattern אסור ל־מישהו = it is forbidden for someone.

So:

• להם = to them / for them
• not הם = they

English turns this into a normal subject:

• They are not allowed...

But Hebrew keeps the person inside the ל־ phrase:

• אסור להם...

If you want extra emphasis, you can also say:

להם אסור לנסוע... = They, specifically, are not allowed to ride...

Because after אסור, Hebrew normally uses an infinitive:

אסור + ל־ + infinitive

So:

• לנסוע = to travel / to go / to ride
• אסור להם לנסוע = they are not allowed to ride

You would not normally use a finite verb here like נוסעים.
So אסור להם נוסעים would be incorrect.

לנסוע usually means to travel, go, drive, ride, depending on context.

In this sentence, because it is followed by על אופניים, it means something like:

• to ride
• to go by bicycle
• to travel on a bicycle

So the exact English wording can vary, but the Hebrew is natural.

Both are possible, but they have slightly different shades of meaning:

• לרכוב על אופניים = to ride a bicycle
  More specifically about the act of riding.
• לנסוע על אופניים = to go/travel by bicycle
  More about movement from place to place.

In many real-life situations, both are fine.
In a rule like this, אסור להם לנסוע על אופניים בלי קסדה sounds natural.

Because in Hebrew, with things like bicycles, motorcycles, and horses, the idea is usually on rather than in.

So:

• על אופניים = on a bicycle
• על סוס = on a horse
• על אופנוע = on a motorcycle

That matches the physical image: you are sitting on it.

אופניים is one of those Hebrew nouns that has a plural-looking form even when it refers to a single object.

Its ending ־יים is historically related to the dual form, and in modern Hebrew אופניים is just the normal word for bicycle.

So even one bicycle is:

• אופניים

And it behaves like a plural noun in agreement:

• אופניים חדשים = a new bicycle / new bicycles depending on context

This is a bit like English words such as pants or scissors, which also look plural even when referring to one item.

בלי means without.

So:

• בלי קסדה = without a helmet

It is a very common everyday word. A more formal alternative is ללא:

• ללא קסדה = without a helmet
  This sounds more formal or written.

Because the sentence means without a helmet, not without the helmet.

So:

• בלי קסדה = without a helmet / without any helmet
• בלי הקסדה = without the helmet (a specific helmet already known in the conversation)

In rules and general statements, Hebrew often uses the noun without ה־, just like English often uses a or no article in general statements.

It means they must not ride.

אסור expresses prohibition, not lack of ability.

So this sentence is about a rule, law, or permission issue.

Compare:

• אסור להם לנסוע... = They are not allowed to ride...
• הם לא יכולים לנסוע... = They cannot ride... / They are unable to ride...

That is an important difference.

Yes, Hebrew word order is somewhat flexible.

The version you have:

אסור להם לנסוע על אופניים בלי קסדה

is neutral and natural.

Other possible orders can add emphasis:

• להם אסור לנסוע על אופניים בלי קסדה
  Emphasizes them
• בלי קסדה אסור להם לנסוע על אופניים
  Emphasizes without a helmet

But the basic meaning stays the same.

Yes. The sentence is built in a very common Hebrew pattern:

אסור + ל־person + infinitive + other details

Here it breaks down like this:

• אסור = forbidden / not allowed
• להם = to them / for them
• לנסוע = to ride / to travel
• על אופניים = on a bicycle / by bicycle
• בלי קסדה = without a helmet

This pattern is extremely useful, and you can reuse it easily:

• אסור לי לעשן = I am not allowed to smoke
• אסור לנו להיכנס = We are not allowed to enter
• אסור להם לדבר = They are not allowed to talk