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I was about to reply though :P I'm glad you understand it know :)
Yeah, I'm pretty curious about S;G0. But I'm also kind of afraid that they will make mistakes, just like in the movie (though that's not canon as far as I know), and mess with the structure of their own world :S I don't really want them to milk this cow :'D

Yes, she should have known about it :)
Keep in mind though that these things are more like theories from me and some others. Not all of these were explained in the VN/anime, but are put together from the things we already knew and from how the world of S;G works :P Only the creators themselves know the full truth, and even they might not know. Maybe it was all just a coincidence that there aren't any plot holes in the story :D

The video mail is still a bit unclear, since every beta world line (at least the ones we saw) Okabe recieved a garbled or corrupt message from the future during the conference (in the very 1st episode as well), but only the one he recieved after failing to save Kurisu was watchable.
Now, there are two theories for these that I've read or know of:
First one is that perhaps the video mail sending device which future-Okabe maid worked in such a way that every world line recieved one of those, but only the one where he fails to save Kurisu got the real one. I don't think this could work since it would imply that the world lines are all existing parallel to each other, which can't be because there is always only one world.
The second one, which I believe might be the case here, is that the "first future-Okabe", who sent back Suzuha, also tried to make and send a video mail, but he couldn't perfect/complete it, because he didn't have enough time. So the message Okabe recieved was corrupt/garbled. The "second future-Okabe", had the time because of obsessing over trying to come up with a plan to save Kurisu. He spent more time on the matter and completed the video mail sending device, so the message was viewable. This could also be even more evidence for the reason Suzuha knew about the video mails. She knew that Okabe needed more time to complete that and to devise the plan for saving Kurisu and destroying the thesis.

Suzuha's whole mission in the Beta world line was to go back to the "present" and make sure Okabe fails to save Kurisu, so that he may develop and obsession with trying to save her, and spend years on coming up with a plan (and the video mail device). The first future-Okabe, who sent Suzuha back probably didn't think about saving her for years after arriving in the beta time line, until world war 3 broke out and he realized that burning her thesis is necessary, and saving her is possible. The first future-Okabe didn't have time to come up with a good plan, but he could finish the time machine with Daru and send back Suzuha so that "the next time", he will have more time to think and plan. Of course we don't see him developing this obsession, since the future already changed when Okabe comes back to the present after failing to save Kurisu (this obsession is what we will see in S;G0).
So the point is, Suzuha knows about the video mail, but doesn't know the full plan and the content of the mail. She only knew that she must make sure Okabe tries but fails to save Kurisu, so that they learn more about the incident involving her death, and about the thesis.

By the reason for existing, I mean that if you look at the very basic concept of time travel, you see that if for some reason someon from the future (like Suzuha) doesn't come back with a time machine, then she can't exist in the present. The best example I can give you is the ending. When Okabe succeeds in saving Kurisu and burning the thesis, Suzuha can't enter the new world line (Steins;Gate world line), because in that world line, she doesn't come back with a time machine. Why would she? World War 3 doesn't happen, so she has no reason to come back. And of course I'm talking about not the Suzuha we see disappearing, but the Suzuha from the future of the new S;G world line :D
I know it can be a bit confusing, but I hope you see what I mean.
Contrary to this, in the world line where Okabe fails to save Kurisu (which is already a different world line than the one Okabe arrives in after deleting the D-mail), Suzuha can still be in the present, because the new-Future-Okabe, the one who made the video mail, sent her back again. But of course this new-Suzuha is replaced by the old one, just like the present version of Okabe is replaced when they time travel. Since she was sent back, she can exist in the present. But in the S;G world line, she disappears because she never comes back, she can't possible be in the present if she doesn't come back. She can't replace herself, or anyone. This is also lets us see that the future of the S;G world line is very promising, and hopefully nothing bad happens (like WW3 or SERN dystopia).

I hope I could clear it up for you :)