It sounds like you have a complicated history that may be difficult to sort through over the internet, but I will give you some thoughts. First off, if your hand tremor and some of your symptoms started after treatment with synthroid (levothyroxine) for your hypothyroidism, I would make sure you are not receiving too much thyroid medication. Too much levothyroxine can make you very jittery, make your hands shake, etc. Sometimes generic levothyroxine can have a different potency than brand name levothyroxine. An endocrinologist can help adjust your medications and make sure you are on an appropriate dose.
As for the PFO and migraine questions, there is an association between migraines with visual aura and PFOs. Visual aura are visual symptoms that begin before or during a migraine. These aura can also happen without the classic headache. There have been studies in which the PFO is closed and these symptoms go away. We don't really know if PFOs cause migraines. It sounds like you don't have the results of your echocardiogram yet, so I would wait to see if this is even applicable to you.
The visual symptoms you are describing could be due to migraines alone. You are right that the hand trembling doesn't seem to fit. I would make sure your thyroid medication dosing is appropriate. You may want to consider switching to brand name levothyroxine to see if it makes a difference. Again, I would discuss this with an endocrinologist. Primary care doctors will often adjust these types of medications, but if you're having this much trouble, it may be worth seeing a specialist.
Lastly, if you are taking any herbal supplements, over the counter medications, etc, make sure you let your doctor know as they can interact with prescription drugs.
Hope this helps!