When you have an error of Access Denied when adding platform Android in Cordova App, just navigate to the folder location in Terminal by cd LocationOfFolder. Chances are that a user logged in the computer has no permission to a node_models folder of an application. So cd into the project folder, then node_modules then Cordova-android folder and enter chmod -Rv 755* in the terminal or command prompt. Note: if you are using Windows, start a command prompt as an administrator.
If you are on mac and android studio doesn't open the Cordova Android project/app, then go to the folder where Android folder/project is and right click and go to "Get Info" then click on the lock, enter your password and change "Sharing and Permission" to "Read and Write" for all accounts.