First I'll answer your actual questions:
Can I start a new sprint without delivering the last one?
During Sprint 2, can I include items into Sprint 1?
No. A Sprint is a timebox. It has a start-date, an end-date, and a Sprint Goal. Once the end-date has passed, the Sprint is done. Without a time machine, it's impossible to add more work into it at that point.
How many undeliverable Sprints can I have in my product?
Please note that, from the Scrum Guide (emphasis mine):
The heart of Scrum is a Sprint, a time-box of one month or less during which a "Done", useable, and potentially releasable product Increment is created.
At the end of every Sprint, your product should be in a state where you could release, if you need to. That doesn't mean that you have to release at any given time.
how can possible many increment exists at same time?[sic]
They can't. Each increment is a Sprint, and each Sprint is a timebox, not a collection of work. You can't have two Sprints co-existing, because Sprint n must end before Sprint n+1 begins. Jan 5 cannot happen at the same time as Jan 6.
I am facing a flexibility problem where the client says that he can change the framework any time and in any way he wants. He argues that Scrum predicts flexibility.
This seems to have nothing to do with an unreleased Sprint. Please either clarify or ask a separate Question.