Hello, I'm new to this and have been doing some research. I'm not sure I fully understand your questions, but I'll take a crack at them.
There are some foods/meds that decrease absorption of levothyroxine which ultimately makes it less effective (so yes that is bad because the goal is to get more T4 - what levothyroxine is - into your system). i hadn't read about avoiding fiber (but here's a link to give you an idea of the types of foods
http://www.mayoclinic.com/health/hig...-foods/NU00582). I had read that iron and calcium can reduce absorption and I try to avoid eating foods with these for 4 hours before and after I take the meds. The best way I've found to do this is to put my pill on the night stand when I go to bed and then if I wake in the middle of the night (I frequently do) I take it - sometime between 4 and 7 AM. This reduces the amount of time I have to wait before I can eat a full menu.
Also I found information (in the link below) that some foods interfere with thyroid function in general and I try to avoid these altogether (not just specifically when I take the meds). The foods listed are broccoli, cabbage, brussels sprouts, cauliflower, kale, spinach, turnips, soybeans, peanuts, linseed, pine nuts, millet, cassava, and mustard greens.
http://www.umm.edu/altmed/articles/h...ism-000093.htm
hope this helps. good luck!