Sharing permissions doesn't apply to sub directories as required
Solution 1:
You've granted everyone the READ permission on the Share. That's all they'll be able to do regardless of your NTFS permissions. Share and NTFS permissions work in tandem to determine the access level of a user when accessing the resource over the network, and the most restrictive combination wins.
You should probably set the Share permissions to Full Control and control access using the NTFS permissions. That's how it's done most of the time.