you do not say "pattern" in Russian:) It is a word that famously can't be translated. In specific contexts it can be substituted with a close-bu-different idea. Узор - is "ornament". Not exactly patternt. Also орнамент. Закономерность - an yet unexplained regularity in events or data. E.g. "each time I do X happens Y" or "when a certain author uses a word X, he soon uses a word Y".

It depends on the meaning, so if it is in the meaning of 1. way - модель [madel'], образец [abrazets] 2. design - узор [uzor], рисунок [risunak] 3. shape - шаблон [shablon]

It really depends on the area of knowledge or context. It might be модель, образец and even паттерн, a literally copy of the english word.

It really depends on the context. Pattern as a template is "шаблон". Pattern as an ornament is "узор" or "рисунок". Pattern as a rule or law is "закономерность" or "закон". Pattern as a sample or example is "образец" or "пример". Also, in modern psychology, pattern is often symply transliterated as "паттерн".

Cesar, "pattern" is a word whose absense Russians can suffer from themselves. When you read about science in English, you find this word quite useful - but often yous see no way to translate it:/