definitely (100%) certainly (100%) very probably (90%) probably (80%) very likely (70%) likely (70%) very possibly (70%) possibly (60%) ? very potentially (60%) potentially (51%) theoretically (51%) * impossibly * not very possibly not very likely (40%) not likely (30%) probably not (20%) ? not very probably (10%) almost certainly not (10%) certainly not (0%) definitely not (0%)
"It will 副詞句 rain tomorrow."
These are also useful for protecting claims from fault. They are often used in "academic" writing for that reason, among other language devices, like this:
"Many computer simulations tend to suggest that seat belts ALMOST CERTAINLY reduce the risk of injury for some people in certain types of accidents, when worn properly, notwithstanding highly unusual circumstances."
I agree with チャリーG-san that "impossibly tall" and "impossibly expensive" are fine. It is more of a modifier for the adjective implying that the state is beyond what is normally expected.
He was impossibly tall - far taller than 'normal' but shockingly so.
It was impossibly expensive - far more expensive than I expected - beyond belief.
There is a difference between use and position of 'hard' and 'hardly'.
Hard - He kicked the ball hard (with a lot of force)
Hardly - He hardly touched the ball (either he didn't get control of the ball in the game very much or he touched the ball but for a very short time or not very hard). The word 'barely' can also be used here.
1) For me, maybe is usually about 50%. It's an all-purpose "yes or no" word that about half the time is yes, half the time no.
2) I'd say that "theoretically" doesn't fit well into that list. It doesn't really express the likelihood of something actually occurring in reality. It's used to highlight the possibility of something from a purely rational / thought-based / speculative point of view, which may or may not have any relation to practical reality.
The fact that "theoretically" it could rain today, tells you nothing at all about the likelihood that it will actually rain today. It could be 1% or 99%.