Sorry, I am very busy today, because I will do school paperbe doing a test. Sorry, I am very busy today, because I will be doing a test.

You can use paper instead of test here but only one of each.

Sorry, I am very busy today, because I will do schoolbe doing a paper test at school. Sorry, I am very busy today, because I will be doing a paper test at school.

This is a more natural way to structure the sentence. Specifying “paper” isn’t necessary.

I can'tdon’t have time to write daily... I don’t have time to write daily...

Your one is correct too! This feels slightly more natural.

Because of this, I can't write daily... Because of this, I can't write daily...

Until you’re at a high level of fluency, it’s best to write in sentences with subjects and complete thoughts. This would sound fine if you are just talking to someone, though.