This may be a weird question and please bear with me, I am completely new into this.
I have a list of 20 requirements (use cases) which I received from my client. With him, I prioritized this list of requirements (1 highest 3 lowest). I wrote for every requirement a use case scenario (rather than user story). I also have a use case diagram and some technical designs (class diagram, database diagram).
Now, my plan is to separate this list of 20 requirements into 5 sprints. Each sprint lasts one week. During every meeting with my client, I can show the product with 4 new use cases implemented. If one of them isn't finished, I move it to the next sprint and my client can request a change during this meeting. During this change, the specific use case diagram and classdiagram/database diagram may be changed.
Is this considered to be Agile? (Even though he gave me the full 20 requirements from the start of the project)
Agile is sort of a big tent, but I would not apply that label to the process you've described. You are describing lots of upfront design work and a full specs up front. The schedule assumes all the req take the same amount of time to implement, thought you acknowledge that it could slip.
The primary agile feature I see is the tight (weekly) feedback loop with client.
I recommend trying on http://pm.stackexchange.com.