I want to release a new version of my game and I already have 6 uploaded files (2 of them are visible) and every time I want to upload, it doesn't create a new file, it just overrides the old one. So I have 2 questions:

Do I need to delete the old file and upload a new one or I can just upload the file and the file will be replaced? If so, will this effect the downloads count?
What is the max. limit of uploading files?

That's right, if a file with the same name already exists, uploading a new one will override it, preserving the download count. Otherwise if you delete it first, the per-file download count goes with it. The project's overall download count is preserved either way.

As for the limit, by default I think it's 1GB for uploading through the browser, and 2GB through Butler, but you can contact support and ask for an increase.