Learn French: Je voudrais poser une question pendant l'émission. - I would like to ask a question during the show.

In French, you don't use demander to say "ask a question". Instead, you literally "pose" a question. The correct phrase is always poser une question.

What verb form is Je voudrais?

It is the conditional form of the verb vouloir (to want). Using Je voudrais translates to "I would like" and is the standard way to make a polite request in French, rather than the more direct Je veux (I want).

Since this lesson is about inverted questions, how would I use inversion to ask someone else "Would you like to ask a question?"

Using the formal inversion from this lesson with the pronoun vous, you swap the subject and the verb and add a hyphen. Vous voudriez becomes Voudriez-vous poser une question ?

Does l'émission mean any kind of show?

It specifically refers to a TV or radio program, broadcast, or podcast episode. If you were talking about a live stage show, play, or concert, you would use a word like le spectacle instead.