On the last point: I take this potassium iodide supplement, which I recommend. (I take one capsule every two days.)

I looked into iodine supplements a while ago—the two main forms are potassium iodide and seaweed/kelp. Two or three legit-looking articles I found said that seaweed/kelp-based iodine supplements can contain very different amounts of iodine to what they say on their labels, which seems like a good reason to be wary. (Additionally, a couple other articles claimed that seaweed/kelp supplements contain high levels of toxic heavy metals, but the veracity of this claim wasn't clear to me.)

The Vegan Society in the UK produce the VEG-1 supplement, which contains 100% NRV of Iodine for an adult (150µg) along with other vitamins and nutrients that might be lacking on a vegan/vegetarian diet

Thanks, I didn't have this on my radar! I'll try to get some iodised salt. 

Thanks, I have iodine supplements but wasn't sure if I should take them because of confusion around how much is too much,

But not being a table salt person looks like I should take at least a little!