Finsweet’s CMS Filter and CMS Load More are what you need.
Regarding the “on a new page” part, that’s possible if you use their URL feature an duplicate / hide the filter fields, but… seems like a lot of unnecessary work to me. From a UX standpoint, consider using the same page with is more in line with the design of these tools also.
I said the client the same and explained that this is wrong. But he still want it that way … And I’ve been struggling to do this already for a few days. Do you know maybe (or have an idea) how to do this on a new page? (how to organize CMS Collection on the “result page”) ? Thank you