Why does Blockchain (the company) open source their code but not license it? I'm very curious as to why Blockchain (the company) doesn't license their open source software. Also, does this mean we (the public) can just use their software and license it using Apache's 2.0 license?

David
If they haven't put a license, it means it is "All rights reserved" You can refer to these questions about it:

https://stackoverflow.com/questions/4007674/whats-the-default-license-of-code-published-at-github

https://softwareengineering.stackexchange.com/questions/148146/open-source-code-with-no-license-can-i-fork-it

https://opensource.stackexchange.com/questions/1720/what-can-i-assume-if-a-publicly-published-project-has-no-license

It probably means "You can use it for yourself, and for small projects. However, if we want, we may shut down all your projects containing our code."