Finding certain elements when only able to ask in chunks
You can eliminate the noise.  Any time you make a query, repeat it 1000 times, use the average of the 1000 responses, and round it to the nearest integer.  The noise in the result before rounding will have variance $1/1000$, so the probability that rounding creates an error is $\operatorname{erfc}(\sqrt{125})$, which is less than $10^{-54}$... i.e., negligibly small (smaller than the probability that a cosmic ray strikes your computer and causes it to give an incorrect result).  This will increase the number of queries by a factor of 1000, i.e., by a constant factor, so it will not affect the asymptotic complexity.
Now once there is no noise, it becomes much easier to solve it.  For instance, you can first find a set of $k$ objects known to be red, then repeatedly randomly sample $n/b$ unknown objects, add $k-n/b$ known-red objects, and query the result; if the response is 1, then you know that one of those is blue, and you can use binary search to find it.  This will require about $O(b \log b)$ queries.  I expect it should be possible to reduce this to $O(b)$ with more cleverness, but I haven't figured that out yet.  A good question is whether you can do substantially better than $O(b)$, if $k \gg b$.