The free offer has a duration of 30 days with 200 dollars of credit and the expiration date is for what is reached first. After that you will upgrade your account to the traditional hiring model called Pay-As-You-GO (paid for use).
Regarding the question of being able to use a free web site the answer is yes, even having a PAYG account, each Subscription has as limit 10 free web sites, 1 Mysql database and another SQL Database with the size of 20MB and valid for the first 12 months of use.
Note:
Relational Database: one 20MB Azure SQL Database and one 20MB Mysql database are available at the Subscription level for the first Twelve months of use; standard rates apply thereafter.
Reference with table demonstrating the limits of free and local Web site where contains the note above: http://azure.microsoft.com/en-us/pricing/details/web-sites/
Only some kind of cost will be generated if you use some other resource, otherwise nothing will be charged.
Good luck and success!
Thank you very much for the information Emerson!
– Eduardo Bottcher