If I purchase the Turbo Tax Deluxe, how many people can use it.

If you are using the Online version, you can only prepare you return(s).  To prepare another return you must create a new account.

If you are using the Desktop version (CD/Download), you can prepare unlimited returns, you get 5 free Federal e-files, after the 5 you must mail in the returns.  Per the license agreement you are the only user of the software but can prepare returns for others.

in creating a new account is there then additional fees per account? 

When you are using the Online version there is a charge for each account (Federal & State return), there is no charge to e-file.