The saying "fit as a fiddle" is somewhat dated in NAmE. I used to hear it more often but I read it in older literature. The word "fit" means that someone is both healthy and ready for action. The word "fiddle" is another word for violin and it alliterates with "fit", both start with "fi". A violin is a precise musical instrument so that a "fit" person is tuned for action as a violin is ready to be played. The phrase "ready and able" is a good alternative.
A "match" is a competition such as a "tennis match". Most sporting events have an official start time so perhaps there is a weather delay or some other reason for not beginning on time.
"I forgot it" means either that it was left behind or that the answer was not remembered. It may not have been learned in the first place. The phrase "I forget it" is wrong though "I forget the answer" can be used though "I have forgotten the answer" better. Note that "I have forgotten" does not mean that something was left behind though it may mean that something was never learned.
If asked, "Do you remember what to do today?" then the reply is probably "Yes, I remember what I have to do". When you say "I remembered it" you should be referring to remembering to bring something. The phrase can be used to answer the question, "Did you remember to bring your homework assignment?"