This is quite an old request and I really suppose that you have solved this by now. But just for the records:
Yes, you can use an extended license on a website. But a standard license is enough for publishing on a website. And yes, when you are doing work for a client, you can't use the same asset again for a different client or an own project, without licensing again.
Look here for more information on licensing: https://community.adobe.com/t5/stock/links-for-licensing-terms/td-p/11366788 (Disclaimer: As always with licensing, this is my interpretation of the rules. I think they are correct and advice is based reading and interpreting the license terms and on fair use for both the buyer and the artist/stock company, but I can not rule out that my interpretation is wrong. I'm not an Adobe employee)
ABAMBO | Hard- and Software Engineer | Photographer