Hi,
1, 2 and 4 definitely are, i'm not sure about 3, skin tends to be dry, thickened and itchy, but not necessarily red or weepy like eczema can be - was the eczema dx by a dermatologist, or a GP?
1 - capillaries repair more slowly, so bruising which is unexplained (from a bump a few days previously you don't remember) and grows over a few days is most common. I think the way blood clots is also affected, as are mineral balances.
2 - in particular sinus and lung, areas which "sweep" clean with mucus, because supressed thyroxine levels slow down those processes, meaning infections can set in more easily. Also fungal things, especially thrush which seems to be because lack of energy makes one more likely to eat sugary food, which makes thrush grow more easily.
4 - PCOS and hypothyroidism often go hand in hand, though i think it might be a chicken and egg thing. When i was most ill and unmedicated i was still ovulating but i had a lot of cysts on my ovaries when i was scanned when PG with DD1.
Hope that helps.