is there a reason this require "doi" rather than just giay?
They're trying to be as specific as possible. Đôi means a pair of something. Giày by itself would just mean "shoes" in general so in order to specify "the" shoes you'd add in "đôi" as a classifier.
Is đôi considered a classifier?
Yes, it's a plural classifier for pairs of things.
If đôi is necessary then a better traduction is "I want to try the pair(s) of shoes". Else it should be accepted "tôi muốn thử giày" without đôi.
Why is saying "toi muon cho thu doi giay" incorrect?
cho means "to give" :)
Program is not accepting thử as correct in above statement.
missing accents on most of these exercises