For most prescription eyedrops, eg. Atropine 1%, there is the warning
"Discard bottle 1 month after opening". I am sure that the medication
is not going to magically change on the midnight of day 30, so my
question is for how many days longer after 1 month can you still use
the eyedrops without losing too much of its effectiveness? What is the
answer if (a) I have been keeping it in the fridge all the time and
(b) I have left it in a humid place of 25 degrees throughout?

You can assume that the eyedrops are new, and they have a
manufacturer's shelf life of 2 more years.

It probably doesn't lose its effectiveness, but might get stuff
growing in it. Once it is opened, it starts to get contaminated, and
any preservatives can only do so much.