The mental health side of things not overly sure about, I am aware that some of the medication used in treatment can cause the patient to be suseptable to T2, and a lot of T1 can suffer from deppression, but this could be control factors playing a part, as well as just living with a chronic disease rather than normal mental illness if you know what I mean...
Yes hypothyroidisum can be linked to T1 diabetes, as they are both autoimmune diseases so if you've got one it could increase the risk of the other, not always though, lot more people who have hypothyroidisum than diabetes..
But the hypothroridisum does effect the individuals ability to lose weight though, as weight gain and struggling to lose is one of the symptoms of it..
Glucose in the urine, isn't the best indicator of diabetes, yes diabetics will get glucose spill into the urine if they have high blood glucose.. But the amount will be dependant on their kidneys threashold of retaining glucose, an good example of this is pregnant women they spill glucose into the urine but when tested it's found that no diabetes involved, they just got a low thrashold..
Only true way of finding out, is a blood test several can be used, a basic finger stick can provide an indicator, then HbA1c to get the adverage and the GTT (Glucose tollerance test) this give a true picture to what is happening to the blood glucose..
I would disguss this all with your doctor, don't be worried about wasting his time as you'll really not, understanding your medical condition is how we find and work out our coping stredaggies (sp) which are very important for our well being..