En cuanto vemos al artista invitado, pedimos una dedicatoria personalizada.

En cuanto means as soon as or the moment. It emphasizes that the second action happens immediately after the first one.

• En cuanto vemos al artista invitado, pedimos... = as soon as we see him, we ask...
• Cuando vemos al artista invitado, pedimos... = when we see him, we ask...

Both can work, but en cuanto gives a stronger sense of immediacy.

Because this sentence most naturally describes a habitual or repeated action. In that case, Spanish uses the indicative:

• En cuanto vemos al artista invitado, pedimos una dedicatoria personalizada.

If you were talking about a future situation that has not happened yet, Spanish normally uses the present subjunctive after en cuanto:

• En cuanto veamos al artista invitado, pediremos una dedicatoria personalizada.

So:

• vemos = we see, as a routine or general pattern
• veamos = once we see, in the future

Not in its current form, at least not in the most standard interpretation. As written, it sounds like a general present: this is what we do whenever that situation happens.

To make it clearly future, Spanish would usually change the first verb to the subjunctive:

• En cuanto veamos al artista invitado, pediremos una dedicatoria personalizada.

You may also hear the second verb in the present instead of the future:

• En cuanto veamos al artista invitado, pedimos una dedicatoria personalizada.

That is also possible in Spanish, because the present can refer to a near or planned future. The key change is usually vemos → veamos.

There are two things happening here:

1. Personal a
   In Spanish, when the direct object is a specific person, you usually use a:

   • vemos al artista
   • not normally vemos el artista

2. Contraction
   a + el = al

So:

• a el artista becomes al artista

This al does not mean to the here in the usual directional sense. It is just the required personal a plus the article el.

Because artista is a common-gender noun. The ending -a does not always mean feminine in Spanish.

The gender is shown by the article and any adjectives:

• el artista invitado = the male guest artist
• la artista invitada = the female guest artist

So in your sentence, invitado tells you that the artist is masculine.

Spanish often leaves out subject pronouns because the verb ending already tells you who the subject is.

• vemos = we see
• pedimos = we ask for

So nosotros is unnecessary unless you want emphasis or contrast:

• Nosotros, en cuanto vemos al artista invitado, pedimos una dedicatoria personalizada.

That sounds more emphatic, like we do that, perhaps unlike other people.

Because pedir means to ask for / request, while preguntar means to ask a question.

Here, the speaker is requesting a thing:

• pedir una dedicatoria = to ask for a dedication

Compare:

• Le pedimos una dedicatoria. = We ask him/her for a dedication.
• Le preguntamos su nombre. = We ask him/her his/her name.

So pedir is the natural verb here.

A dedicatoria is a short personal message written for someone, often in a book, on a photo, CD, poster, or autograph item. In this context, it is something like a personalized inscription rather than just a plain signature.

Personalizada means it is made specifically for the person receiving it, for example with their name or a custom message.

So this is more personal than just an autograph.

Because in Spanish, most descriptive adjectives normally come after the noun.

• una dedicatoria personalizada
• un artista famoso
• una canción bonita

Also, personalizada agrees with dedicatoria:

• dedicatoria is feminine singular
• so the adjective is personalizada, also feminine singular

You could move some adjectives before the noun in Spanish, but that often changes the tone or sounds more literary. Here, una dedicatoria personalizada is the normal order.

Yes. In fact, that is very natural if you want to make the person receiving the request explicit through a pronoun:

• En cuanto vemos al artista invitado, le pedimos una dedicatoria personalizada.

Here, le means to him / to her.

The original sentence leaves that pronoun out because the context already makes it clear who the request is directed to: the guest artist. Spanish often omits information that is obvious from context.

You could also say:

• ...le pedimos una dedicatoria al artista invitado
• ...pedimos una dedicatoria al artista invitado

but the original version is perfectly natural if the context is already clear.