Your first condition is already in licenses like the Apache 2.0, GPLv3 and several other licenses. However, it isn't a requirement that "the patents are in the public domain" (mainly because such a requirement doesn't make sense, the public domain is a term used in copyright law to refer to a work with no copyright, it has nothing to do with patent law). Rather, it states that all contributors grant a "perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable" patent license to any other user of the software, provided that they do not attempt to sue a user for infringement of patents that were granted under that license.

Your second condition would make the license a proprietary licence (it violates freedom #0: the right to run the program as you wish without restriction). In addition, I'm not sure that it would enforcible with current copyright law (similar to the provisions in the AGPL), since I'm not sure you can argue that input data to a program is something that you could restrict in law (and if it's free software, the end user can modify it to allow you to break that rule). And it would also be a minefield (what if something could be patentable, or is patented by someone other than the person who distributed it, what if the patent holder gave a patent grant to the rest of humanity, how many requirements are there for such a grant in order for it to be allowed, etc).