Isn't the neuter adjective zvláštné? Also, is "mě" pronounced as "mně" in Czech?
It is not, just "zvláštní".
You're right, "mě" is pronounced exactly as "mně".
Is there a reason why zvláštní ends in í not é?
There are two types of adjectives. Soft (ending "í" in the nominative singular for all genders) and hard (ending ý/á/é in nom. sg. depending on the gender of a noun they develop). Read Tips and notes, there is more about it.