The answer to all three questions is yes, if you have a good thyroid doctor that will treat you clinically (for symptoms) by testing and adjusting Free T3 and Free T4 as needed to relieve symptoms, without being constrained by resultant TSH levels. Obviously your Free T4 and Total T3 are too low in the range, indicative of being hypothyroid. You can also get some good insight from this link written by a good thyroid doctor.
http://www.hormonerestoration.com/Thyroid.html
Members say that symptom relief requires Free T4 at the middle of its range, at minimum, and Free T3 in the upper part of its range, as needed to relieve symptoms. In addition hypo patients are frequently too low in the ranges for Vitamin D, B12 and ferritin. D should be about 55-60, B12 in the upper end of its range, and ferritin should be about 70 min. Low levels can cause symptoms that mimic hypothyroidism. Low D or low ferritin can also adversely affect metabolism of thyroid hormone. You need to get those tested and supplement as needed to optimize.
Since your doctor tested for Total T3, not Free T3, and also did not test for TG ab, the other test needed to rule out/in the possibility of Hashi's, I am not too optimistic that he is the good thyroid doctor you need. So, before possibly wasting time there, you need to read the above link and then call the doctor and find out if he is willing to treat clinically, as described, and also willing to prescribe T3 meds like Armour Thyroid and Cytomel, if that becomes necessary. If not, then perhaps we can help locate a good thyroid doctor for you.