It's WINE and dine -- it's not truly an idiom. It really means to take someone out and treat them to wine and fine dining. You see this phrase used most often when someone is trying to curry favor by paying for someone's night on the town.
sine dine
"To be" is not an idiom - it's a verb.
I think it is £1000
The Idiom actually reads 'Fighting tooth and Nail'. It means to give everything you've got, literally every tooth and nail in your body, to win a struggle.
Just what it seems to mean - someone has taken someone else out for drinks and dinner. You often hear this said of business acquaintances, that you "wined and dined' them during a business deal.
Pest is not an idiom. It's a word.
Doing anything "by a hair" means that you barely manage it. If you win by a hair, you win only by the margin as wide as a hair is. If you lose by a hair, you almost won. You can also have a "close shave," which is an idiom meaning that you escaped something bad by a hair's width.
The idiom "apple shiner" means the teacher's pet.
The meaning of the idiom in the pink of health means being in good health.
chew, dine
The idiom means impress someone is egg on
It's not an idiom - to cope means to deal with, or to handle