How long will it take my legs to get used to walking 16+ miles a day?

At that amount of distance, you will always notice some soreness. Even highly trained athletes would be sore after walking 16 miles-- especially because you are using your joints to stay upright for an extended period of time. However, it will be less intense over time. If you are collapsing at the end of a walk due to leg-jellies or soreness, I would recommend training up to that distance. Over training can just cause muscle exhaustion and, just like with running, stress, tears, and injury.

Start with half that distance... if you can complete that and feel tired but not exhausted, then keep it up for a week or two. Every week or two add a mile.

Although your body COULD get used to walking 16 miles a day if you start there, it will take longer and be more stressful (and you will be more prone to injury) than if you start at a shorter distance and work your way up.

Is not eating enough calories causing an underactive thyroid?

There are more likely causes of an underactive thyroid, but if you severely limit your calorie intake, the chance that you lack dietary iodine to make thyroxine in your thyroid is quite possible. Iodine is commonly added to table salt to avoid this, how much salt do you eat?)Either way, your diet is probably

Which is more important, health, wealth, happiness, or freedom?

That's a little like asking whether food or water is more important. Without either one, you die. The only criterion you could use to decide which is more