It just means your best - the image is of you making sure that your best is totally level and perfect in appearance.
No because the meaning is obvious: you are trying your best at something.
The best way to find out the meaning of an idiom is to look it up in a reputable dictionary or idiom database. You can also search online for the idiom along with the word “meaning” to find explanations and examples of its usage. Additionally, asking a native speaker or language teacher for clarification can help you understand the idiom better.
Show your better side, be the best you can be
"To be" is not an idiom - it's a verb.
The literal meaning would be that you have one foot that is "the best" and you're tossing it out ahead of you.
It means you did your best and were honorable; you didn't cheat or anything.
Pest is not an idiom. It's a word.
The idiom "apple shiner" means the teacher's pet.
The meaning of the idiom in the pink of health means being in good health.
The idiom means impress someone is egg on
It's not an idiom - to cope means to deal with, or to handle
"Old hand" is an idiom meaning having lots of experience.