Most of what you present here is not in the form of a question. You start with this:
1 When we talk about one person, one thing, one event and then we refer back them, we will use "he, she, they, it", not "this, that, the".
- I met my friend last night
- Were they a doctor. (not that person / this person / the person)
Here, you are making a statement, not asking a question. I disagree with the premise of your statement, and I find your example ungrammatical.
In the first sentence, I would use "met with", "met up with", or "saw" rather than "met". Although not ungrammatical, "met" by itself usually has a very strong implication of meeting for the very first time.
It has become widely accepted to use a plural pronoun such as "they" in many instances where there is a singular referent whose gender is unknown. This is not one of those times. I can't condone any permutation of "they are a doctor".
These all work better as the rejoinder:
1a': Is he (or she, if the gender is known) a doctor?
1a'': Is your friend a doctor?
1a''': Is this person a doctor?
Please note that all of my examples are presented as questions and are punctuated with question marks. I use the present tense rather than the past because I haven't been given any reason to believe that the friend has died, or otherwise ceased to be a doctor. And I have no problem referring to the friend as "this person". I might also have said "this friend that you speak of".
You go on to say:
2 When we talk about more than one thing, person, event ... and then we refer back them, we will not use "he, she, they, it", we can use “the".
- I bought a cat and a dog yesterday. I will give John the cat and I will breed the dog.
Again, you are not presenting this as a question, but as a statement of fact. Your use of ellipsis (" ... ") in your premise statement indicates that you are quoting from another source rather than formulating your own ideas. If this is true, you need to cite your source.
That being said, your example is grammatically perfect. I will point out, though, that the subject-case pronouns "he", "she", and "they" would not work here, where the referents are all direct objects of the verb.
(3) is the only issue that you actually present as a question:
3 When we talk about more than one thing, person, event ... and then we refer back them, we will not use "he, she, they, it", so can I use "that, this, these, those” as “the” ?
- I bought a cat and a dog yesterday. I will give John that cat and I will breed that dog.
- Last night, when I were talking with a girl, suddenly a man approached and hit me. Then that girl ran away and that man chased after.
- (On the phone) I am choosing beetwin buy a cat or a dog, this cat is pretty and this dog is a little fierce.
I would like to restate this more grammatically:
III: When we speak of more than one thing, person, or event and then refer back to them, we do not use "he", "she", "they", or "it", so can I use "that", "this", "these", and "those” instead of “the”?
a: I bought a cat and a dog yesterday. I will give John that cat and breed that dog.
b: Last night, when I was talking with a girl, a man suddenly approached us and hit me. Then the girl ran away and the man chased after her.
c: [On the phone] I am choosing between buying a cat or a dog. The cat is pretty, but the dog is a little fierce.
Regarding (IIIa), I don't like the demonstratives "that", "this", "these", and "those” in this context. They imply that there are other cats and dogs being discussed, so that these need to be singled out from among the others. You should word (IIIa) exactly as you did your example in (2). Again, though, the subject-case pronouns don't work. If you were doing the same thing with the cat and the dog, you could say:
IIIa': I bought a cat and a dog yesterday. I will give them to John.
IIIa'': I bought a cat and a dog yesterday. I will breed them.
Examples (IIIb) and (IIIc) work exactly as I have written them.
In discussing (4), I'm going to refer to the "last week" dialog as "(a)" and the "three years ago" paragraph as "(b)".
4 Or I only can use “This / that / these / those” to refer back all details of an event or whole paragraph.
- Last week, there was a bat flew into my house and I broke my mirror.
- OMG! Those were bad omens. (refer back whole the above paragraph)
- Three years ago, I met an accident last night. The driver dozed off at the while, he bumped the guard line. That accident (refer back all details of the accident ) changed his lives.
In (4a), the first speaker should either say "there was a bat that flew into my house", or even better, "a bat flew into my house", leaving out the phrase "there was".
I have no problem with the second speaker commenting that "those were bad omens". You should be aware, though, that "OMG!" is an abbreviation of "Oh my God!", and there are many that find this offensive. Certainly, such colloquialisms are inappropriate for any type of formal writing.
In (4b), the first sentence is self-contradictory. The accident either happened "three years ago" or "last night", but not both. If you are able to look back to it now and say that it "changed his lives [sic]", my guess is that "three years ago" is more accurate.
I also prefer "met with" or "was involved in" over "met".
In the second sentence, I think you mean to say "wheel" rather than "while". The sentence also contains a comma-splice error, in which two independent clauses are joined by a comma. There are many ways of fixing this, but the simplest is to rephrase it as:
The driver dozed off at the wheel and bumped the guard rail.
In the third sentence, I would find "the accident" acceptable, but I admit that "that accident" sounds better to me. In either case, the accident "changed his life" or "changed our lives", but it did not "change his lives".
Did I leave anything out?