It'll be interesting to see Obie's response. I've never seen a jet "jump-started" by another plane although have seen and experienced the odd flight when the first engine was started by an external power source - I think that can happen when the APU may not be working. As for the smoke, maybe it was a new engine? They come with extra lubricants that need to be burned off and make an awful lot of smoke, e.g.,
https://youtu.be/ZEPhgZeZARI?si=wR2OJanh-l7x0eo6
https://youtu.be/faTt0hIjjg8?si=PqoA1Y0RmVdcmqmM
https://youtu.be/ZEPhgZeZARI?si=wR2OJanh-l7x0eo6
https://youtu.be/faTt0hIjjg8?si=PqoA1Y0RmVdcmqmM