can or something else

     I don’t know when “can” or “may” or “might” or something else is the right choice. I basically use “can” but now I’ve written a bunch of example sentences where I feel that the “can” is not the same kind of “can,” therefore in many cases it may be a wrong choice. First:
What can be in this room? (I mean: I wonder what is in this room?)
     In the following sentences “can” is intended to mean “probably”.
Let’s take this screwdriver, it can be useful. (I mean that for e.g. during our journey.)
He can talk about a cat. (I think he is talking about a cat.)
Its function may be to… (Now I’ve still written “may”. I mean “I think that its function is to…”)
     And now too, I almost wrote “can,” but maybe “must” is better: The fence defends the area against wild animals. That trench must have the same value.
He may try to repair the car. (I think that what he does at the car maybe is: he tries to repair it.)
     I’m not sure that the following is the same case.
When this town is mentioned, its main square also can occur to us.
     Though not in the same way, but the following also seems to be about some possibility:
Just like ox or horse, some dogs can also be draught animal.
     And here is the very important and more problematic part:
The name of this animal is eagle ray. Its swimming resembles the flight of the eagle, that is how it can be called eagle ray. (I mean that I’m not only think so; I can also say, „that is why it is called eagle ray. I just think that „can,” or something else can express something like „in this way it is possible that it is called eagle ray.”) Plus another question: Is “called” important in this sentence? Would it be a correct sentence without it?
Or (something similar) : Superman saves everybody. That is why he can be Superman (Of course, I could also write that “that is what makes him Superman,” or “that is why he is Sm.” But I feel that the sentence with “can” contains something like “that is what authorizes him to be called Sm.”
[After mentioning all the processes happening in the womb: ] “That is how one can be born.
She always loved cycling. That is how she can come with a bike now too.
God can be God on the principle that he created and operates everything.
Only the other side of the car was smashed up, that is how he can live even now.
     The following is again a different category, or isn’t?
This can be more understood from the following story.
     And see the following sentence.
He may be so happy because of the drink he has drunk. (I mean that I think so.) But I think I can say, “He can be so happy because of the drink he has drunk” – then meaning that it’s a fact that he is happy due to the drink.
I’m sorry for writing so much but I feel every sentences a bit different, regarding the word “can.” So I’m very confused.