El permiso de rodaje afecta a la vía pública.

El usually means we are talking about a specific permit, or about the filming permit as a known thing in context.

• El permiso de rodaje... = the filming permit...
• Un permiso de rodaje... = a filming permit...

In administrative or formal Spanish, the definite article can also sound more natural when referring to a category in a general way.

In Spain, rodaje commonly means filming or shooting, especially for films, TV, adverts, and similar productions.

So permiso de rodaje is the normal Spanish way to say filming permit or shooting permit.

This is more idiomatic in Spain than trying to build the phrase from grabar or filmación.

The de links two nouns and shows what kind of permit it is.

• permiso = permit
• de rodaje = for filming / related to filming

This structure is very common in Spanish:

• permiso de trabajo = work permit
• licencia de conducir = driving licence
• tarjeta de crédito = credit card

So permiso de rodaje is literally something like permit of filming, but naturally translated as filming permit.

Because the subject is el permiso, which is singular.

The full subject is El permiso de rodaje, but the head noun is still permiso.
De rodaje just adds extra information; it does not change the number.

So:

• El permiso de rodaje afecta... = singular
• Los permisos de rodaje afectan... = plural

With this meaning, Spanish normally uses afectar a + noun to say that something affects someone or something.

So:

• afecta a la vía pública
• afecta a los vecinos
• afecta al tráfico

This is one of those verb patterns you mainly have to learn as a chunk: afectar a.

Because in Spanish only a + el becomes al.

• a + el = al
• de + el = del

But a + la does not contract.

So:

• a la vía pública is correct
• al vía pública is wrong

Vía pública is a fairly formal or administrative expression. It usually refers to public roads, streets, or public thoroughfares.

It is broader and more official-sounding than just calle.

So depending on context, it can mean things like:

• the public street
• the roadway
• the public highway/road network
• public space used for traffic and access

In official language, la vía pública is very common.

Because in Spanish, adjectives usually come after the noun.

So:

• vía pública
• permiso especial
• zona peatonal

Putting the adjective before the noun is possible in some cases, but it often changes the tone or meaning. Here, vía pública is the normal fixed expression.

Because vía is pronounced in two syllables: ví-a.

The accent mark shows that the i is stressed and forms a hiatus with a, instead of merging into one syllable.

So it is pronounced roughly VEE-ah, not as one syllable.

This is the same kind of spelling pattern you see in words like:

• día
• país
• frío

Yes, it sounds quite formal and administrative, especially because of expressions like permiso de rodaje and vía pública.

This is exactly the kind of wording you might see in:

• council notices
• permit applications
• official regulations
• municipal websites

A more everyday sentence might use something more informal depending on context, but this version sounds very natural in official Spanish from Spain.