Why does line current become half when load becomes half of full load in a dc shunt motor?
In a dc shunt motor, the field resistance is generally very high. This is to avoid high current through field. On the other hand, we require high current through armature. Practically, you will find field resistance values in 100s of Ohms while armature resistance will be less than 1 Ohm or so. So, due to high field resistance, current through field will be very low compared to armature current.

So, as line current = armature current + field current, and field current is negligible compared to armature current, we can approximate line current to armature current.

Yes, torque is proportional to armature current in a dc shunt motor. So, when load increases, armature current increases and we can say that line current also increases by almost same amount because (again) field current is negligible compared to armature current.

Also note that, generally in Electrical Engineering, we refer to load as load current and not the impedance or other properties of actual load.