Who wrote the actual bitcoin software? Who wrote (and owns) the actual bit coin mining code?

If the origins is not crystal clear, it will be very difficult to explain its use to ordinary everyday people.
You can find a list of contributors to the official bitcoin software here: https://github.com/bitcoin/bitcoin/graphs/contributors

Over 160 people have contributed to writing the bitcoin software, not counting the ones like Satoshi him/themselves who wrote the initial version of the program. 

But the important part is that many more people have actually read and reviewed the source code. You can review it yourself if you learn how to program, and judge for yourself that the software is doing what it actually claims to do.

So it doesn't matter at all that we don't know who initially wrote it.

If you read or heard about a great idea somewhere, would you discard it simply because you don't know who actually had the idea? If the idea is useful and it makes sense, it should be used regardless of the creator.