Green tip cuttings less than 5 or 6 inches in length can sometimes be rooted in small pots of damp soil or water. However, larger woody-stemmed cuttings that you are asking about really have to be air layered if you want to propagate them. Air-layering is a bit complicated and may be something you would rather not do.
Your tree looks terrific after its summer outside. Now is the time to prune it back sharply - as much as you can stand. The pruning will help it better fit inside your home and also help it adjust to the greatly reduced indoor light. You may also consider pruning out the interior small stems as they are shaded by the outer canopy of leaves and are the first to fall in reduced light.
