Though we use both 'under' and 'below' to refer to a place/thing lower than the other, but 'below' is used for greater distances and 'under' for smaller gaps.

To perform beyond one's expectations means on or to the far side of something; farther than expectations. Further is not the correct usage.

Phrasal usage. 'To crawl along' means to move across something on hands and knees.

Case of idiomatic usage. 'To come across someone or something' means to find someone or something. 'Come around' means to revive; recover.

The clue here is 'and he arrived' which shows that 'I was just going to call him when he arrived'. Preposition 'about' is the best usage in this case.

For specific point of time we use preposition 'since', while 'for' is used for period of time'.

Idiomatic usage. 'Fan out' means to spread over a wide area .

To refer to a specific point of time of the past we use preposition 'since', while 'for' is used to refer to a period of time.

'To be through something' means to reach the end/destination or to achieve success.

The sentence implies that all the efforts were fruitless. Preposition 'but' is the correct usage here.

Phrasal usage. 'To search for someone or something' means to look very hard for someone or something.

Idiomatic usage. 'Once upon a time' means once in the past.

When one work is almost to happen at the time of occurence of the other, we use preposition 'about' for the first one.

Preposition 'without' means with avoidance of. Nobody can live by avoiding the use of water. Thus, 'without' is the correct usage.

For nations, continents, and large cities we use preposition 'in', while for specific places, small towns etc we use preposition 'at'.

Phrasal usage. 'Quest for someone or something' means to seek after someone or something.

Preposition between is used in case of two. We sometimes keep our money between two leaves of paper of a book. And that is what referred here.

The sentence implies that snakes sleep during the whole of winters. Preposition throughout is the correct usage in this case as it means during every part of something.

In this case we mean that the book is lying on the bed; but in case of persons we generally prefer 'lying in the bed' as it includes not only the bed underneath but also the sheet/blanket over us.

We make 'amendments to' something.

The word 'separately' is always followed by preposition 'from'.

Beside means to the side of something or someone, while besides means in addition to something or someone.

Here, preposition 'in' will be used with 'comes'. "During" and "throughout" means 'from the beginning to the end of'. 

Here, the key word is 'all'. 'All, but him' or 'All, except him' is the correct usage, which means all were present there, excluding his son.

Against means in opposition to someone or something. In elections two candidates stand in opposition to each other. Thus, option 1.