Does happiness increase accuracy because it seems that my Pokémon never miss attacks they are supposed to
miss;Articuno never misses Sheer Cold, other don't miss Thunder. Does happiness have a factor in this?
No, it does not. Happiness has no effect on accuracy. Something that may have been a factor in what you've seen is level; Sheer Cold becomes more acurate the higher your level is opposed to the foe. Also, if it's Raining thunder will never miss. Or you could just have really good luck :)
No, happiness does not affect any stats. Happiness effects the evolution of certain Pokémon, the power of Return and Frustration.
http://bulbapedia.bulbagarden.net/wiki/Happiness here's more information.