int mid = (low + high) / 2;
but you'd have to constrain low and high to be in the range [-2^30, 2^30 - 1] so as to not overflow a (assuming 32-bit) signed integer. (And you're probably using 64-bit floating point, or similar, which has other fiddly bits.)
I found the most helpful reframing is to replace the words and emotions with ones that encourage learning and question-asking. For example you can try being excited instead of surprised, or say something like, "that's a great question, let's figure it out together."
Going through the Fermi estimation in the xkcd comic Ten Thousand also helped me to be a lot less genuinely surprised when someone didn't know something: https://xkcd.com/1053/