I am new to dwarf fortress and my question is how does armor user skill and strenght affect encumbrance? (I know that more armor user skill or strenght is better but I want to know how EXACTLY they affect it ; for example which armor is ok to wear at which skill level).How can i know if my dwarf is encumbered and how does this affect combat?
I 'm afraid I can't give you exact answers to these questions, however I can suggest you a (sort of) rule of thump based on my experience. I've found that when I gave full, metal, armor suits to (very) weak dwarves with no armor skill, they will virtually halt their training (too encumbered or too tired to spar effectively). Limiting their equipment to just
a helm, a mail shirt, gauntlets, a pair of boots (all made of metal) and a cloak had been enough to get them going again while providing (in theory) full body coverage. Assuming encumbrance affect sparring in the same way as actual combat, I'm guessing that (without factoring in martial trance) giving these dwarves too much armor early on is practically a death sentence.
Also, (again based on sparring observations) it seems that encumbrance is less of an issue either for (very) strong dwarves with 0-3 in armor user or for average to strong dwarves with 3-5 in armor user, so I would assume these would be the minimum limits before you can issue them full metal armor suits.
Of course you can always supplement the above basic equipment suggestion (bold) with breastplate and greaves made of leather/bone for added protection without adding too much weight.