The newel is easy, do what you already have planned for that area, and add a few drills 1'8 inch holes around it also.I would then use a polyurethane glue that will expand a little when it goes into the holes. Something like Gorilla glue works great, Then in those little holes, you put some round thick toothpicks to help fill. I fix antique chairs and tables like this all the time for customers. Works like a charm.
That spindle you will need to get a little more creative. Also with the glue, install a dowel that will go down into the spindle/(if there is a hole there) and up into the rail.