quote:1- He wake up from sleeping.
You are correct, Sayed. The verb should be in the past tense: woke.
However, "from sleeping" does not belong in the sentence. When you wake up, clearly you have been sleeping. So just say this: "He woke up."
quote:2- Feeling tired, went to bed early
Yes, you are right again. This sentence is not correct. The verb "went" needs a subject. The subject could be I, you, he, John, she, Mom...anyone.
So, "Feeling tired, I went to bed early" is correct.