About Free files of week.

Can we publish directly the free of week project to google play store by adding ADS to the project..

Yes, no problem.

Do remember that App templates are Templates for creating new apps and are not meant to be uploaded as there are.
Do make sure you reskin the item. add new features or make sure you add some value. Otherwise is would not have any added valiue to the app store, because there is already a identical item and it will be rejected.