Learn Spanish (Latin America): Hay que solicitar el documento que tiene el cónsul. - One must request the document that the consul has.

Because we are talking about a specific, existing document that the consul definitely has (el documento). We use the indicative tiene for facts and real things. If we were looking for any document that the consul might have, we would use the subjunctive: un documento que tenga el cónsul.

Why is the word order que tiene el cónsul instead of que el cónsul tiene?

In Spanish, it is very common and natural to put the verb (tiene) before the subject (el cónsul) in a clause that starts with que. While que el cónsul tiene is grammatically fine, native speakers usually prefer the word order shown here.

Could I use pedir instead of solicitar?

Yes, but solicitar is a better fit here. Both mean to ask for, but solicitar is more formal, translating closer to to request or to apply for. Since this sentence involves a consul and official paperwork, the formal word sounds much better.

I remember hay, but what does hay que mean?