Learn Portuguese (Portugal): Quero que o debate seja durante a palestra. - I want the debate to be during the lecture.

No, it doesn't! Unlike prepositions such as de or em (which merge with a to become da or na), the preposition durante (during) never combines with the article. They simply sit side by side: durante a palestra.

Why does the sentence use seja instead of é for the verb "to be"?

Seja is a special form of the verb ser called the subjunctive. You don't need to master all of it yet, but the key trigger here is the phrase Quero que... (I want that...). When you express a desire or wish for someone or something else, the following verb must change from the normal present tense (é) into this subjunctive form (seja).

Why doesn't the Portuguese sentence use the infinitive ser like the English "to be"?

In English, we say "I want [object] [infinitive]" (I want the debate to be). Portuguese does not use this structure. Instead, you always have to phrase it as "I want that the debate is" (Quero que o debate seja).

What exactly is a palestra? Is it the same as a class?

A palestra is specifically a talk, a presentation, or a guest lecture. If you are talking about a regular, everyday school class or a standard university lecture, you would use the word aula instead.