It's not an idiom because it means exactly what it seems to mean. To take offence at something means to be offended or insulted by the something, so "did not take offence" means the opposite.
"Take you out in a box" is an idiom for "murder" in that you will be carried away in a coffin.
It is a Caribbean idiom meaning to be mislead and conned into a silly situation.
It means that you "Take a look" or to look at something.
"To be" is not an idiom - it's a verb.
"Take heart" means to be courageous or hopeful, to think positively
Pest is not an idiom. It's a word.
To take the most possible out of the system using it to your absolute advantage.
It means to take control of something and maybe get it working again or improve a situation.
The idiom "apple shiner" means the teacher's pet.
The meaning of the idiom in the pink of health means being in good health.
Can you figure out the meaning by defining the terms literally? No, so it is an idiom. Literally, it means to remove something, but figuratively it means for an airplane to get off the ground.
It's not an idiom. It's a pithy saying. In order to be an idiom, it has to have a meaning exclusive of the actual words used and be easily understandable only in the culture it originates from.