Learn English – I got you vs I’ve got you

Yes, this is a mistake. I can see 6 Google results for "we are also be talking about", but four of those are from the same (possibly Chinese?) source, one also looks to be Chinese, and the remaining link is an automatically-generated transcript from a video, and therefore cannot be trusted to be correct.

The correct phrasing is "But we are also talking about...". The extra "be" is wrong because the verb "to be" is already present in the form of "are".

To answer your remaining questions: "we will also be talking about" is correct because "will" is necessary to signal that we are talking about the future. Other tenses don't use "be" like this, so "we were also be talking about" is incorrect.

As a native speaker, I have to say that I would never use the second sentence, "Did you see what they had done to our city?", except to describe a state of the city that has passed. For instance, if someone had painted a wall, I would ask a friend, "Did you see what they have done to our wall?". If that paint was then washed off, the question would be "Did you see what they had done to our wall?" as that state of "painted" has passed.

As for the difference between sentences three and four, I do not see any. It's just as correct to say "Did you see what they have done to our city?" as it is to say "Have you seen what they have done to our city?". However, I would say that if you asked somebody returning from the city, you would say sentence three rather than sentence four, as "Did you see" implies that they could have seen as opposed to "Have you seen" which implies that they may not have had the chance yet.

For instance, if somebody went to a cinema the same day that a new film was showing, I'd ask "Did you see that film?". If we were talking about the film, and I didn't know that they'd been to a cinema, I'd ask "Have you seen that film?".

As for the fifth sentence, you're absolutely on point.