Lets start from the beginning:
"Are these sentences correct?"
"The best job for Julia is to work as an English tutor, because its flexible work". OR "the best job for Julia is an English tutor" - add the "an" to sound more natural
"and doesn't take much effort to learn how to do it" - lets change this to "and doesn't take much effort to learn how to do". I don't think you need to add the "it". It feels wrong to end this sentence with "it", because you've already talked about the subject - and ending with it just replicates the subject in the word "it" (email me if this doesn't make sense... I feel that this needs more explanation). Even better still is "and its easy to do". This is a simple sentence which says everything you wanted to say and is a powerful way to end this thought. Your original sentence was very good none the less!!
"it agrees with her busy schedule" - English is fine - no problem there.
the biggest mistake you made was your original question: "Is these correct sentences?" The present tense plural "to be" verb is "are". Then swap so that you have "are these sentences correct"
Otherwise your fundemental English is good.