1. Can neurons in the brain handle 2 separate tasks? I think the answer is yes; http://oc1dean. Blogspot. Com/2011/11/neuronal-multitasking-principle. Ht

Yes. It sounds like you know the answer to your question. Multitasking is an essential brain function. Listening and writing is one example. Interpreting (listening, comprehending and speaking) is a good one as well.
Multitasking is real. We all are able to handle more than one task at a time but some are much better than others. This is not a single neuron issue but more a complex interplay of neuronal functioning that we develop over time.