Nature: Well, Nature can be called ‘Qudrat’, but proper word for nature is ‘fitrat’ as Qudrat includes nature but is not confined to nature.
Mother nature:
For Muslims (also Jews and Christians), Mother Nature is God.
For pagans, they might have particular god as Mother Nature, a god who determines natural laws and looks after natural events.
For Scientists (also Agnostics and Atheist), Mother Nature is laws that govern the universe (or Laws of Physics).
Anyhow, even though you did not ask, I feel obliged to explain (according to my knowledge and understanding) a bit about your first question, so to clear confusion.
Nature = fitrat
It is inherent character that Allah has given to groups of similar creations, be that creation living or not.
[Lion do not like to climb tree, Cat loves milk, Males are attracted to females, Sun gives light, fire burns, snow is cold etc … so, these are nature (fitrat) of Lion, Cat, Male, sun, fire, snow, etc].
Character = Mizaj
Something particular species (group) do not necessarily have as fitrat but is capable of, so selective in that species might have it as character different from the group as whole.
[Particular Lion loves to climb trees, Particular cat do not like milk, particular male do not get attracted to females, fire that do not burn, etc … so, these would be character (Mizaj) of that particular Lion, cat, male, or fire, etc]
[To show sadness hearing bad news, show happiness hearing good news, show anger when agitated, is nature of human. Anyhow, some people do not show sadness hearing bad news, do not show happiness hearing good news, do not show anger when someone try to agitate them, and since any or all in a human is not norm, it is not considered natural (fitrati) but it is considered character (Mizaj) of these people.]
Miracle = Muajza
It is neither natural, neither can be classified as character. Even though Muajza happens for short time, it could be a continuous happening. Anyhow, when something happen continuously in certain species (or sub-species), it could be classified as fitrat in that species (or sub-species).
[Lion stop eating meat and start eating grass, Cat start flying, Male gets pregnant instead of female, rock floating on water, etc
Note: It would be considered as Muajza if male gets pregnant instead of female, though surprisingly this is normal in two fish species (that I know) and thus for those species it can be classified as fitrat of those fish species.]
Extra-ordinary/unexpected = Karishma
This word can be used for miracles/Muajza. [Hindus might use it to define Muajza). In Urdu (or amongst Muslims) Karishma is not normally used for Muajza, rather for anything that can be defined as possibility (due to it being fitrat, mizaj, or natural events), still happening was unexpected or extra-ordinary. For instant, if anything happens that is unexpected, extra-ordinary or beyond belief than it gets referred to as Karishma.
Qudrat: English has no particular word for this Arabic word (as far as I know), but can be defined.
Definition = Will of Allah.
Everything that exists or happens is ‘will of Allah’, so, everything is Qudrat, but normally word is used when a person wants to emphasise about it referring to something extra-ordinary or beyond belief. Occasionally, people wrongly use ‘Qudrat’ in place of ‘Fitrat’.
Qudrat includes … Fitrat, Mizaj, muajzat, Karishma, events, and whatever. (Natures, characters, miracles, extra-ordinary events, etc)