What are your policies regarding ownership of computer code in your lab?
I can only comment on your first question. Since you work for a large US-based institution I would be surprised if they do not have policies regarding IP generated by using university resources. That is, it may not be up to you to decide how ownership is handled. Many big universities have their own office to deal with technology licensing, patentable inventions, and so on. Since (in my limited understanding), this is a huge legal minefield, I would recommend contacting them first before you set any policies that you cannot keep. This is even more so if any external funding is involved, since funding agencies might also want a piece of the pie.