Try setting up your existing free Yahoo account on the iPhone as a Yahoo Push-IMAP account.
Go to Settings > Mail.
Select Add Account.
Select Y!Mail or the Yahoo Mail selection at the top.
Enter your Name, current Yahoo email address, current password for this account and your chosen description or account name for the account.
Not sure why you can't connect to YouTube - on occasion the same happens to me but I retry and all is well.