You don't need to. You now have permission to use the corpus in perpetuity, according to the terms of the licence. In the past, the BNC was made available on optical disks, and users had to pay for a licence. Now it is free, and you just have to agree to abide by the terms of the BNC user licence.
No, commercial companies are welcome to use the corpus in the same way as anyone else, as long as they abide by the terms of the BNC user licence.
Yes, and we would like to encourage this. You are not allowed to make the corpus texts available, but you can make fragments and derived lists available. So, for example, concordances which show a maximum of a few sentences at a time are fine. It's also permitted to publish wordlists, collocations, clusters, keywords, visualizations of distributions of features, etc.. If you don't want to develop your own tools, you could make your own installation of BNCweb.
Yes, provided you don't quote more than would normally be regarded as ‘fair use’. For citation information, see Referring to the BNC.