1. The guests talked about a lot of topics on the talk show.

2. The guests talked about a lot of topics in the talk show.
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Which one is correct? Do we have to use 'on' here?

3. First speaker, come to the podium, please. And deliver a speach about the topic.
(Is this passage correct? In fornt of a classroom, when there is no raised part made of wood, can we use 'podium' as in the first sentence? What is the name for the part on which a lecturer put his textbook? It is on a floor which doesn't have a flatform.)

You should use "on" in the first example sentences.

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3. First speaker, come to the podium, please, and deliver a speech about the topic.
(I made a couple of corrections.)

In front of a classroom, when there is no raised part made of wood, can we use 'podium' as in the first sentence? (Yes)

What is the name for the part on which a lecturer put his textbook?
(It's called a lecturn.)

It is on a floor which doesn't have a platform. (Such a raised platform could be a dais or a stage.)