Learn Italian: Qualcuno ha l'adesivo, vale a dire la colla speciale? - Does anyone have the adhesive, that is to say the special glue?

Vale a dire literally translates to it is worth saying, but it functions as a set phrase meaning namely or that is to say. It introduces a clarification of the previous word. You could absolutely use cioè or ovvero here, though vale a dire sounds slightly more formal and precise.

Would in altre parole work here instead of vale a dire?

It would sound a bit unnatural. In altre parole is typically used to rephrase an entire idea or complex sentence. When clarifying a single specific noun like l'adesivo, markers like vale a dire, ovvero, or cioè are the correct choices.

Why did the speaker feel the need to clarify l'adesivo with la colla speciale?

In everyday Italian, l'adesivo is most commonly used to mean a sticker. While it is also the technical word for an adhesive substance, the speaker uses vale a dire to ensure people know they want the special glue, not just a sticker.

Why is the verb ha singular when the speaker is likely asking a whole group of people?

The indefinite pronoun qualcuno translates to someone or anyone, and it is strictly singular in Italian. It always requires a third-person singular verb, no matter how many people you are talking to.