Whatcha mean....create a new account in what
You can create a Free Skype Account!
You don't need a Facebook Account to get a Skype Account!
You do not create a new account on your iphone. Instead you login with your existing account that you use on your laptop. Then they will be synced.
There's a option when signing in.
What error are you getting? Take a Look at Skype's Help Pages and see if you can find the Answer to your Problem There!
Go on the skype web site (see related link) and download it. After you downloaded it, open it and under the username it says something about that you don't have a skype account so click on it.
To establish Skype password first you have to create an account in skype with following instruction and if you want to change the password of skype then first you log in on skype with using the user name and password then Click on "Help" in the top menu then select "About" to find out which version of Skype you are using. After that click on file, then click on My skype account then click on change password then enter new password and click on OK to save the password.
Download the app and follow the instructions to create it
No you cannot. You would have to create a new account for a new name.