hey hey vnav i,ll give you all the answers you need to all the questions i will email them to you. In answer to this question though. I believe it is two-fold
1.) To prevent large supercooled droplets forming on the engine intakes i.e formong clear ice which can disrupt airflow into the intakes. Hence icing conditions exist at TAT +10.
2.) and I think more importantly the heat created at the intakes warms the moist intake air so it does not cause icing on the fan blades which can obviously lead to disrupted airflow, compressor stalling, and vibration. I hope others can clarify these points somewhat.