It is typical of the British. I suspect it is British/Indian in origin & is descriptive of a lack of emotion, or at least visible emotion. Apparrently it comes from the novellist PG Wodehouse in 1924, or at least it was popularised by him.
This is not an idiom - it means exactly what it says. You should stay fit and healthy.
To keep struggling and not give up.
Stay calm
Keep bothering someone.
It means " keep calm, don't get worked up"
Keep an idea in ones head to act on it later.
The more common idiom is "stiff as a board," meaning "very stiff." Unless used ironically, like "straight as a crooked stick" or "straight as a politician's promise," the expression "straight as a board" would mean "very straight." When referring to "straight as..........." the term usually is as straight as a die
This is not an idiom. When you compare two things by saying one is the other, it is a metaphor. It means that however you keep your house reflects your personality, and vice versa.
There isn't an idiom called "eggs basket." Perhaps you are thinking of the old proverb that says "don't keep your eggs in one basket."
The image is of you pointing an eye at something or someone. It means to watch carefully.
It means to be on the lookout for a street by the name of Connecticut.