The root "твор-" (to create)

One of the things I have found with language learning - and particularly with Russian - is a tendency to 'plateau', to reach a particular level and then not to make progress. One manifestation of this is that there are particular mistakes which I keep making and I can't seem to overcome. Often all that is required is to research a bit, find out the correct answer and to start using it.

The basic verb is творить (imperfective) which means
(1) to create (synonym создавать/создать) or
(2) to do (synonym делать/сделать)

Here are some examples of the second meaning (slightly old-fashioned or churchy): 

• Он творит добро. He does good (i.e. performs acts of kindness).
• Что ты творишь? What are you doing? What are you up to? 
• Они не ведают, что творят. They know not what they do (Biblical quote) 
• In contemporary usage the same verb can be used to mean 'do something strange': Он может что угодно с тобой сотворить. 
• In formal church use it can me 'perform': сотворить молитву, сотворить крестное знамение. 
• Что ты натворил? What have you done? 

The first meaning is the translation of the English 'create': Бог сотворил мир. 

If you want to talk about the ongoing process of creating (When God was creating the universe...), you can either say, "Когда Бог творил вселенную," or, "Когда Бог сотворял вселенную..." 

The noun сотворение (eg сотворение мира) refers to the act of creating. The pairing "creation or evolution" would translate as "сотворение или эволюция" (I am not proposing to discuss whether these are indeed opposites or mutually exclusive). 

The noun творение refers to the end-product, the creature. An old-fashioned word тварь (fem.) used to bear the same meaning but now refers to a person who is wild or beast-like ("подлый, мерзкий человек"). The modern word is зверь (masc.). There is also the expression "все твари в паре" which refers to a motley crew or diverse bunch of people. 

The adjective тварный means created; the theological concept of uncreated is нетварный or несотворенный. 

God the Creator is Творец (or Создатель); by analogy a human artist may likewise be called a creator.

Творчество is both creativity and the fruits thereof (творчество Пикассо = the work of Picasso).