Fraggle, you had written so much that I am difficult to understand.
You
have written so much that
is difficult for me to understand. -- or -- ... that I am having difficulty understanding.
Do you have a PhD in language?
No. I only have a B.S. and it is in accounting. But I have been studying languages and linguistics since 1954, when I was 11. Many (perhaps all) of our Moderators in the "hard science" subforums (Physics, Biology, etc.) are professionals in their fields with advanced degrees. But that's not true in all of the other discussion topics.
I'm also the Moderator of Arts & Culture. I don't have a degree in any of the arts, although I am a part-time non-career professional musician.
1. He has no friend other than me (or I?).
This sentence is not really incorrect, but we would almost always say, "He has no
friends other than me."
"Me" is correct, rather than "I." When a pronoun follows "than," you have to look back in the sentence and find the first word in the comparison.
"He is taller than I." "He" is the
subject of the sentence, so it is in the
nominative case. Therefore "I" must also be in the nominative case. This is true even if the subject is a noun; nouns are not inflected for case like pronouns: "My wife is smarter than I."
However, this grammatical rule is often broken, especially in speech. Most people say, "My wife is smarter than me." In writing, I strongly recommend that you learn to use the words properly and say "smarter than I." Learn correct English first, then you can experiment with colloquialisms and slang.
Back on topic, your sentence starts with "He has no friends..." "Friends" is the
object of the verb "to have." Since it is a noun it is not inflected for case, but you are comparing it to a pronoun. The pronoun must be in the accusative case because it is also acting as an object of the verb. So, "He has no friends other than
me."
2. He has no friend beside me.
First off, pay careful attention to the difference between:
- Beside. Meaning: at the side of, alongside, near. When I take my dog for a ride in the car he sits beside me, rather than sticking his head out the window as some dogs do.
- Besides. Meaning: in addition to, other than. Besides rock and roll concerts, I also go to hear symphonies and chamber music. This restaurant offers a full menu, besides our award-winning cakes and pies.
So: "He has no friends besides me." Again, we would say "friends" instead of "friend." I would only put it in the singular when using an idiomatic expression: "I have no idea why Alex isn't here yet, besides the possibility that he's stuck in traffic." "Melinda has no talent besides the ability to always look beautiful."
Not bad vs. good. Do they mean the same? If you think it is really good, why not just say good instead of "not bad"? Is this cookie tasty? Not bad! Or Good! ???
They don't mean the same at all. You need to focus on the difference between an
opposite and a
negative. My dog is not small, but at 20lb/9kg he is not big either. A small dog weighs ten or twelve pounds (4-5kg), a big one weighs at least 40lb/18kg. (Standards vary from one culture to the next; in France a dog probably has to weigh less than 5lb/2kg to be called "small."

)
When we say something is "not bad," that is almost a colloquialism. We could mean literally that it is merely not bad, but there's no way we would classify it as good. "This food is not bad: it won't make you sick." But it's also a way of giving a
grudging compliment: "I can tell that you've finally gotten serious about studying your math lessons. Your score on the last test was not bad."
Finally, there's what we call
damning with faint praise.
Professor, what did you think about my children's musical performances?
Rose, Aidan and Neal were very good!
Okay, but how about little Casey???
He was not bad.
1. I have hope in God that he will deliver me. -- 2. I have hope on God that he will deliver me.
You have hope "in" someone or something, not "on" him or it. However, your sentence is very awkward.
I have hope in the future. I believe that one day there will be no war, hunger or racism.
You can say, "I have hope in God. I believe he will deliver me." But most people would say "faith" instead of "hope," when they're talking about a person, whether it's a real person or a mythological person.
I have faith in George and his crew. I'm sure they will finish painting the house long before the rainy season.
3. I believe Jesus vs. I believe in Jesus, got difference in meaning?
Gigantic difference.
- To believe someone means that you trust what he says. You think he's an expert in his subject, or at the very least you don't think he's a liar.
- To believe in someone is quite different; it has several slightly different meanings.
"I believe in Atlantis (or King Arthur)." This means I believe that it was a real place (or that he was a real person).
"I believe in President Obama." This means I trust him: I think he's an honorable man who will try to do what he promised.
"I believe in the Texas Rangers." This means that even though they lost the World Series this year, I have faith in their coaching and team spirit, and might win next year. (I'm making this up, I know nothing about baseball and had to use Google to even find out who played in this year's World Series.

)
"I believe in democracy." This means that I think that democracy is the best way to provide people with freedom and good government.
"I believe in Mayor Gray." This means that even though the police keep discovering illegal things he's been doing, I still think he'll do a good job of running the city.
To
believe someone means you think what they say is correct. To
believe in someone is to have faith in their existence, honor, skill, etc. You can also
believe in a place, a thing, a concept, etc.
"I give you the benefit of doubt" means what?
"I give you the benefit of
the doubt." This means that I don't have enough information to decide for sure whether you are correct/honest/skillful, etc. But I will
err in your favor and assume that you are.
This is the basis of the U.S. (and other countries') legal system. If you are prosecuted for a crime, the government must present evidence
beyond a reasonable doubt that you are guilty, before it can convict you and punish you. Otherwise, even if it looks
very likely that you commited the crime, that's not enough to convict you: you get
the benefit of the doubt.
However, we do not limit the use of this phrase to the legal system.
- Susan, I see that your husband is installing the new spa. I thought you were going to hire a contractor?
- I was, Sharon, but Keith said he could do it.
- But Keith has no experience with that kind of work, does he?
- I know. But he did a pretty good job building our doghouse.
- A doghouse? A spa is a much bigger project. Besides, doghouses don't have plumbing! How can you trust him?
- He's my husband, Sharon! I have to give him the benefit of the doubt. Besides, the city inspector will come and look at it before we're allowed to invite you and Roger over to use it. If there's something wrong it will be the inspector who accuses Keith of doing bad work, not me!