Maybe, perhaps, possibly, probably. Do they mean the same thing and can be interchaged?
No. "Maybe," "perhaps" and "possibly" have the same meaning, but "probably" is different. The first three mean that it could happen or it could not happen, and you're making no statement about which outcome is more likely. But when you say "probably," that means
at the very least that the probability of it happening is > 50%, so it is
more likely to happen than not happen. But the way most of us use it most of the time, it means that the probability is
much greater than 50%. There is a chance that it won't happen, but it's a small chance so we'll be surprised if it does not.
1. Maybe it is going to rain.
This sentence is grammatically correct. But if you're using an informal word like "maybe" instead of a more formal word like "perhaps," it would be more consistent to use the more informal contraction "it's" instead of the formal expression "it is." Try to be consistent.
And then, of course, if you are trying to be formal, you should use the more formal construction "will rain," instead of the informal phrase "is going to rain."
So choose: "Maybe it's going to rain," or "Possibly it will rain."
2. Perhaps it will rain in one hour time because the sky is dark.
This is not correct. You have to say either, ". . . it will rain in
one hour because . . . ." or ". . . . it will rain in
one hour's time because . . . ." There's no rule for this, you just have to copy what we say.
3. It is possibly to rain today because of the dark cloud in the sky.
This is very wrong. "It is possible that it will (or may) rain today. . . ." or "It may possibly rain today . . . ." are both correct.
Also, "cloud" should almost certainly be plural, "clouds." If I see
only one dark cloud in the sky, that is not enough evidence to predict rain, unless it is so big that it fills the entire sky.
4. Probably it will rain very soon because humidity is high.
This is incorrect. "Humidity" is not one of the many nouns that can be routinely used without the definite article. You have to say "the humidity is high" in most cases. There are other cases where you don't need it, but I'm not going to write an entire article here.
Putting "probably" first is not exactly wrong, but it's awkward. We would say "It will probably rain . . . ." It would be okay to put "maybe" first: "Maybe it will rain. . . ." This is another one of those cases where there is no rule to explain the difference, you just have to mimic the way we speak.
If you want to stress the fact that you think it is
almost certain that it will rain, then you could put "probably" first, but since you would stress the word in speech (say it loudly), you should stress it in writing by putting in a comma: "Probably, it will rain very soon. . . ."