This week I should look aroundt the various “Zemi” (seminars)” and decide which Zemi I belong to.

If you include extra bits in the quotes, like here, it can give the impression that it is part of the quote. Since this is an aside to give an additional definition, it is best placed outside the quotes.

“Zemi” isare different from classes.

I feel like here "Zemi" is acting as a plural (which would agree with "classes") so it should be followed by "are" instead of "is".

It is taken overThey are done with a few people (5-9 people), and in which we debate on certain topics, gathering somea few times in a week.

Looking at the Japanese text you used 研究 which to me would imply research or study rather than debate. But because I'm not sure exactly I'll leave it like this.

AreIs there a similar system in your universities?

You could also ask if there are similar systems, but here since you're talking about a single system I felt it most natural to use singular.

And, if so, what do you call it?

Adding this extra bit to help connect it to the previous sentence. This type of construction is very common when asking a question that depends on a previous one.