Well, for starters, we need to have an understanding of what the Thyroid gland is… and the Thyroid gland is a gland that controls our body’s metabolic functions. It does so, by taking iodine from the foods that we consume, and producing T3 and T4 hormone, which are absorbed by the body’s cells. How much hormone the Thyroid produces is a delicate balance, and it is dictated by the Pituitary gland. As the body needs more T3 and T4 hormones, the Pituitary will produce higher levels of a hormone called Thyroid Stimulating Hormone, or TSH, which signals to the Thyroid gland that it needs to make more of these hormones. Inversely, as the body needs less, the TSH levels will go lower. The TSH in itself, is merely a level indicator of your thyroid hormones, and of your Pituitary function. It holds no other function than that.
When your T4 levels are supplemented from outside, the TSH level will go down because the Pituitary gland will notice that, and it won’t need to “scream” so to speak, at the Thyroid gland anymore, to make more T4… It will NOT drop the levels of T4.
What can happen, sometimes, is that some Doctors only test for T4, and do not test for T3… so sometimes, folks still have symptoms after being on a medication for a while. 25 mcg of Syntrhoid are only a starter medication, and honestly, it takes a little while for the meds to have an effect on our system and for us to feel better. This can be anywhere from 6 weeks, to 6 months. You will likely not be upped by much, in my opinion, as your TSH was really not that high at all. For comparison’s sakes, I was diagnosed at 150.0 TSH level. I have to take 125 mcg daily. Synthroid is a medication that will only supplement T4. If your T3 is also impaired (which, you see an endocrinologist for this, and not a GP), you will need to take a medication which has both T3 and T4, like Armour Thyroid. Another thing to keep in mind is that if you have any antibodies present, those can throw off the results of a TSH… and a good Endocrinologist will need to go by your overall symptoms, your Free T3, Reverse T3, Free T4, and entire metabolic profile levels, to adjust your medication more appropriately.
As to your other questions, your doctor is absolutely WRONG. Thyroid medications need to be taken on an empty stomach, and preferably 30 minutes before eating, as many foods we eat which contain calcium, iron, fiber, and large amounts of iodine, can interfere with the body’s ability to absorb the replacement hormone. Such foods as kelp which are extremely high in iodine, should be avoided, and foods like unfermented soy products, because they are goitrogens – they can enlarge the thyroid, impair hormone absorption, and worsen Hypothyroidism. Limit yourself to fermented soy products, like miso, and tempe, etc. Tofu, and soy milk are NOT okay.
In some cases, Levothyroxine has been known to interfere with blood sugars. Some people will need twice as much basal as before, and some people have reported having low blood sugars, in contrast. Every person is different with their response, and you will need to be extra watchful with your blood sugars as you are taking this medication.
I invite you to join the group, Hypothyroid Diabetics, so you can ask questions of people in your same position, learn more about the Thyroid, and have people to relate to as you go on this new journey. 
