Student or Learner
Could I use the words in brackets, or can I leave them out? Is this text correct anyway?
(The) Children can join into several activities of our courses according to their talent and (their) expectations.
The aim and (the) task of the education of arts and crafts is to improve the children's ability to express their own imagination and (their) feelings by creating objects.
You can leave "the" out, unless you are referring to a specific group of children. "Their/s" can also be omitted as you indicate.
The sentences are fine.