1) He was in a light mood for he had just rested from his hard part-time job.
I think this is fine.
2) It was my painstaking for your good. What a pity that you don't understand it.
I don't think painstaking is the right word there, but I can't think what it should be instead (sorry).
3) After speaking what is on her mind, the girl couldn’t face directly the boy.
This doesn't work. Keeping the sentence as simmilar as possible, you could say "the girl couldn’t directly face the boy", but I think that it's more common to leave out the word directly - "the girl couldn’t face the boy"
4) One day dragged by, so did the other day and the third day.
The sentence is not perfect, but I think dragged by works there well enough.
5) To her great disappointment, she received nothing from him. Though the girl supposed that it was to be so, it was too much for her to accept it.
Hmmm, I'm not sure what to suggest here.
6) Receiving the bad news, she went dull.
If I understand what you're trying to say here, I think "numb" would be a better choice instead of "dull".
7) He tried to fade his ex-girlfriend from his memory.
Try "eradicate" instead of "fade".
8 ) You should focus on something really matters.
Try: You should focus on something [that] really matters.
I hope that helps, even if it's incomplete.