1. A better way to phrase this is to use active voice, not passive:
His friends expect him to be discharged today.
"I hadn't got" is an awkward phrasing. You can make the sentence better this way:
I wish I didn't have two tests tomorrow.
2. "by yourself" or "youself" -- either one works fine.
3. This sentence needs to be completed. When you use a comparative adjective or adverb without completing the thought (earlier than what?), your listener or reader will be waiting for the rest of the sentence!
Would you mind if I stop working ten minutes before closing?
Would you mind if I stop working ten minutes earlier than you do?
Would you mind if I stop working at ten minutes before 5:00 pm?
In the passive sentence, you can keep the "by __" or leave it out. From sentence to sentence, you'd need to decide if that information is needed or not.
My sandwich has been eaten!
My sandwich has been eaten by someone.
My sandwich has been eaten by a thief.
4. Yes, when you're talking about age, you'll need to indicate it somehow.
My dog was only six months old.
My dog was only six month of age. [stilted language, not often used in casual speech]
Yes, "all the things" is fine.
I can't do all the things myself.
I can't do all the housework myself.
I can't do all the yard work myself.
I can't do everything myself.
5. Your correction is correct.
I wish he didn't have to work.
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