Why does tummo decrease metabolic rate?  When practicing tummo, would consuming amounts equal to Total Daily Energy Expenditure or slightly above raise metabolic rate?

Without addressing how Tummo works, I will answer the other question; consuming more calories does not increase metabolism.

If one were to do regular anaerobic exercise to counter the catabolic effect of tummo, similar to countering the catabolic effect of aerobic exercise, and eating enough protein to maintain / gain muscle, would one not have an increased metabolic rate?  Let's assume that tummo is used to maintain temps of around 98.6 degrees while sitting still on a cold day.

Question #2: If one becomes very experienced in tummo, would it not be possible to multitask ones thought process on other complex tasks while practicing tummo?

you are begging the question of the specific metabolic mechanism involved in tummo. The other question I have is What's your purpose in manipulating your metabolic rate? Why, what for, what does it let you do, etc?

My initial interest in tummo was becuase I have hypothalamic-pituitary-adrenal axis disregulation such that my cortisol and T3 is low and as a consequence, metabolic rate is low.  By increasing body tempurature to normal levels via tummo I am hoping that this will provide the energy to help maintin an optimal metabolic rate, perhaps with the addition of moderate anerobic exercise to offset the catabolic effects of tummo.

I'm getting hung up in your terminology. As best I understand it "catabolic" implies a specific process/mechanism. If all you really mean is that tummo can result in decreased metabolism, or reduced metabolic rate, then I can look at your question differently.

For example, there are specific breathing patterns which temporarily raise metabolism, blood pressure, pulse and temperature. Fighters sometimes use them to "throttle up" right before their round begins. And there are breathing patterns to take you back down again, to recover a normal heartrate and pressure between rounds.

If one becomes very experienced in tummo, would it not be possible to multitask ones thought process on other complex tasks while practicing tummo?

I would imagine so. 

Let me ask a somewhat different question, if I may. Is your interest in Tummo solely or mainly based on raising body temperature, or is it a desired by-product of the spiritual endeavor?

If your interest is more focused on raising body temperature, there are autogenic methods which are somewhat quicker to accomplish, and easier to call on from time to time during daily life.