The free offer has a 30-day running time with $ 200 credit and the expiration date is whichever comes first. After this you will upgrade your account to the traditional contracting model called Pay-As-You-GO.
As for the question of using a free web site, the answer is yes, even if you have a PAYG account, each subscription is limited to 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.
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 the free and locall Web site where it contains the above note: link
Only some kind of cost will be generated if you use some other feature, otherwise nothing will be charged.
Good luck and success!