Rav Chaim Kanievsky Shlita does not use the internet at all even in the way you stated. I think that if you were to ask him, he would tell you that ideally it is better not to use it at all (by ideally, I mean that if a person could accomplish the same thing with or w/o internet, he should not use internet).
No shaychus to burka women. As far as I understand, all the Gedolim are against wearing burkas and do NOT consider that to be tznius. Their wives do not dress that way.
The wives of Gedolim do not wear black nailpolish. It is not accepted in the Torah community.
Tznius is something that is not always black and white (no pun intended). One has to develop a sensitivity to it. It is true that most people do not have the right sensitivity and therefore some people can reach the wrong conclusions (in either direction). That is why we have Gedolim – to guide us and tell us what is tznius and what is not (although we should try to work on our sensitivities as well).
There was a famous story with Rav Moshe Feinstein, Zatsal. Someone asked him about a certain style. He said that it was absolutely untznius/assur (I don’t know what lashon he used, but I think he meant both). The man said, “So why doesn’t the Rav publicize that fact? All the Frum women are wearing it; obviously, they don’t realize it’s untznius.” Rav Moshe responded, “Most people care more about what the fashion makers in Paris have to say than about what Rav Moshe Feinstein says.”
What is scary about this story is that it shows that there may be many styles that everyone is wearing that may be completely untznius and assur and no one realizes it and the Gedolim are not saying anything about it (and keep in mind that this story happened in Rav Moshe’s lifetime when the standards of tznius were much higher than today).
That is why we have Gedolim – to tell us what is tznius and what is not, since we can’t always tell ourselves. We know that burkas are a problem because they say so.
However, another interesting thing about this story is that in fact, Rav Moshe chose not to publicize that this style was untznius because he knew the oilam wouldn’t listen. That is kind of why I am not comfortable telling someone that something is assur if I see that they will not listen plus it is something that I personally (although I could be wrong) am not certain that it is assur, but I think it is something to strive for (and even that much I only said because I was asked).
btw, the reason that I put black nailpolish in a different category than other aspects of tznius is because I think the only issue involved is that it sticks out as opposed to being untznius for the kinds of reasons that most untznius things are untznius. I see “sticking out” as a sensitivity level type of thing. One is not supposed to wear something that sticks out (one of the problems with burkas btw), but I don’t know if I can tell someone that it is 100% assur (again, when talking to a young girl who clearly is not holding by it yet.)