Just know that roots don't adsorb water but water vapor.
Never heard this before. Do you have a reliable source for this information?
The plant is a bit young to do drastic pruning if you want the trunk to grow indeed.
I am worried that the die-back might be due to its current location. If it is indoors over a heater, this may cause drying out of leaves. Also, fertilizing as much as you are fertilizing now is too much. Some peoplke seem to think of it as food. It really is more like vitamins. The fertilizer contains some specific elements that a plant needs to grow. but the energy to grow comes from the foliage. I would just give it optimal care. Allow it natural light, with a few hours of direct sun each day. Stay away from air conditioners and heaters and other appliances that dry out the air.
If you have a spot outside where the plant would not get direct sunlight, you could consider putting it there outside. But I understand your worries re. the summer sun, having lived in Australia for a few years myself. I do not know how elm would respond to it. Here summer temps peak at 35, 38C. That is never a problem. The tree just drinks water by the liter, and watering twice a day is a must in those temperatures. It looks like you are not in the driest parts of Australia, and I think it would be fine in a sheltered spot between the trees, out of too much wind (It is often the wind, and not the temperature per se that kills the plant; The leaves just cannot get the water fast enough)