IDA Pro and bninja are totally different. Indeed, bninja is dedicated to static analysis, wherease IDA provides both. According to their website, bninja will provide such feature when their static engine will be entirely done and, apparently, the development process is far for being finished.
No, not at this time. We definitely plan for a debugging interface in the long term but right now we are focused on our static analysis efforts.
Of course, that hasn’t stopped others from integrating Binary Ninja into a dynamic analysis workflow. For example, check out Snare’s Binjatron plugin that connects Binary Ninja to Voltron which itself is a front-end for a variety of debuggers (GDB, LLDB, WinDbg and VDB at last count).