Busybox is GPLv2. That's the same license as the linux kernel; it's not a problem. You just have to release your modified version of the busybox source if you distribute it in a product. The only difference is that busybox developers enforce the license against the many companies who can't be bothered and respond to requests with lawyers.

That said, a bsd-licensed re-implementation of busybox (still in c) that's pretty far along and has gotten support from some of those companies (including Sony) is "toybox" http://www.landley.net/toybox/

There is a busybox in Go. https://github.com/surma/gobox

What licensing problems specifically do you mean here?