I can't open my folders in yahoo mail on my iPad 3. Tried tapping on folder icon, which goes to folder list, but can't get into them.

If you are tapping the folder icon towards the top right of the Mail screen next to the flag icon, then that is to file the currently displayed email i.e. to move that email into the folder that you then select, not to navigate to view a folder. You need to tap on the links at the top left of the list of the emails (depending upon what you are viewing it might be 'Back', the email account name) to go up the email folder/account hierarchy, and then navigate down to the account/folder that you want to view.