I really have the following doubts. Can you see if my corrections are OK? Thank you.

1) He is expected by his friends (is wrong?) to be discharged today.
I wish I hadn't got (Is this possible?) two tests tomorrow.
2) Do you always make breakfast by yourself/yourself? (without the help of his parents)
3) Would you mind if I stopped working ten minutes earlier (not before)
My sandwich has been eaten by someone. (should "someone", "people" be omitted in the passive sentence?)
4) My dog was only six months (is "old" necessary?)
I can't do all the things (is "all the things" correct, all the housework, everyhing) myself.
5) I wish he hadn't to work at the weekend. (Correction: he didn't have to work)

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.

Let's go through each statement and correct them if necessary:

1) He is expected by his friends (is wrong?) to be discharged today.
The statement is grammatically correct. "He is expected by his friends" indicates that his friends are expecting him to be discharged today. No correction is needed.

I wish I hadn't got (Is this possible?) two tests tomorrow.
The sentence is almost correct. However, instead of "I wish I hadn't got," it should be "I wish I didn't have." So the corrected sentence would be: "I wish I didn't have two tests tomorrow."

2) Do you always make breakfast by yourself/yourself? (without the help of his parents)
The personal pronoun "his" seems to be incorrect here because it doesn't match with "yourself." The corrected sentence would be either "Do you always make breakfast by yourself?" (if speaking to one person) or "Do you always make breakfast yourselves?" (if speaking to multiple people).

3) Would you mind if I stopped working ten minutes earlier (not before)?
The statement is correct, and "earlier" is suitable in this context. The sentence expresses a request or inquiry about leaving work ten minutes before the usual time.

My sandwich has been eaten by someone. (should "someone" or "people" be omitted in the passive sentence?)
The sentence is grammatically correct as it is. However, you can omit the "by someone" part without changing the overall meaning. So the revised sentence would be: "My sandwich has been eaten."

4) My dog was only six months (is "old" necessary?)
The word "old" is necessary in this sentence to provide complete information about the dog's age. So, the sentence should be: "My dog was only six months old."

I can't do all the things (is "all the things" correct, all the housework, everything) myself.
The phrase "all the things" can be replaced by "everything" to convey the same meaning. So the corrected sentence would be: "I can't do everything myself."

5) I wish he hadn't to work at the weekend. (Correction: he didn't have to work)
The correction is accurate. The phrase "he hadn't to work" should be changed to "he didn't have to work." So the correct sentence becomes: "I wish he didn't have to work at the weekend."