Goodness! Talk about the deaf leading the blind! Neither of you really knew what you were talking about.
Levothyroxine - L-Thyroxine - Thyroxine - all the same thing (never mind the prefix - levo - L - it's complicated). It is thyroid hormone, usually called T4 because it has four iodine atoms - as I said before.
But I have to ask you... You say how can a blue powder be a hormone - well, what did you expect a hormone to look like? It can be in powder form or it can be in liquid form, but it's still a hormone. Not a drug.
When the man in B&H told you not to take iodine with thyroxine, what he meant was - although he probably didn't know it - that if you take thyroxine, you're already taking iodine, and too much iodine is bad. That's why you shouldn't take it with thyroxine, not because there's some terrible reaction between the two.
Also, although he probably didn't know this, either, taking iodine when you are hypo can lead to further complications.
I explain all this above - I think I may be the 'guy' you're referring to - but I'm a goose, not a gander - but I think you largely chose to ignore it.
If you've been on Thyroxine for 7 years, and feel no better, and not getting any answers from your doctors, I think it's time you asked for all your blood test results - with the ranges - for as far back as possible, to see what's been tested, and what the results were in figures. Not just your doctor saying 'it's fine', because doctors rarely know what they're talking about, when it comes to thyroid, either.
Get your results, post them on here, and we will be able to tell you whether you are on the right dose or not. Although, it sounds to me that your dose is too low and/or you aren't converting that thyroxine (T4) to triiodothyronine (T3) - which is the active hormone, needed by every single cell in your body, and which they Don't appear to be getting at the moment.
As to iodine 'eating' fat... do you know why? Because, if you take iodine, it stimulates your gland to make more hormone, and it's that hormone that makes you lose weight (which probably isn't even fat, anyway). But that effect won't last forever. Eventually, you will crash. And you will crash hard.
So, let's have a look at those blood tests, shall we? And find out what's really going on.