I’d like to clarify the (somewhat squishy) data.
First, I’d like to get rid of the possible parenthetical reading (especially because the Russian punctuation makes it look like English parenthetical).
Suppose the situation is that Ivan visited many countries. So many that it is kind of hard to believe. Now, maybe previously Sandy said that Ivan visited 140 countries. But later Sandy added that in fact Ivan himself had said he only visited 135, and later Kim said something about 140 but that is less reliable. Now we are talking to Sandy and we want to establish how many it is that Ivan visited for sure.
(8) How many countries do you know for sure that Ivan visited? [eng]
In Russian, I can maybe say this in the following way:
(9) ?Ivan skolko, ty tochno znaesh, chto posetil stran?
Ivan.NOM how.many 2SG for.sure know.2SG that visited countries.PARTITIVE
"How many countries do you know for sure that Ivan visited?" [rus]
I think that (9) may look strange out of context but I also believe that it is entirely possible (and hopefully it is less confusing than (6) because it is clear that the “you know” thing is not parenthetical).