Try These! - Imperatives

The simplest answer is best here; any of the other suggestions would be understood, but none of them is quite what we would say.
If you want to include yourself in a group, to do the thing that you're suggesting, you simply put 'Let's ...' on the front of the sentence. When you are ready to start out, you can say 'Let's go!' (= iVamonos! in Spanish; 'Allons-y' in French)

The doctor won't be able to see down your throat if your mouth is shut; and the wider open it is, the easier it will be for him (or her) to look.

The best way to do this is to say:
(Please) do not + VERB*
(* or verb-phrase; the action that you don't want people to do.)
We will give you another question like this later in the Quiz.

Most of the words here are short, simple ones that could be used either as a noun or as a verb. For an instruction, the first word in each phrase must clearly be a verb.
'Slow' is usually an adjective ('a slow train') but there is a phrase 'Slow down', a bit like 'sit down', which means to take things a bit more gently.
The correct answer has extra strength because each half of it starts with the same letter, S.

You need to start by breaking the eggs first, so none of Answers 1 - 3 would work!

It helps if you start by saying 'please'!
In English we don't just 'hear' music, we 'listen to' it (certainly if we have paid money to enjoy that experience). We can't just 'listen something', 'we have to listen TO it'.
(You may have heard a famous old pop-song called 'Downtown', where the chorus begins: 'Listen to the music of the traffic in the city ... ' ~ but if you have been learning English with real people, perhaps in a class rather than from a book or online, we are sure you will have heard a teacher say 'Listen to me' ~ or perhaps 'Please listen carefully to me' ~ on many occasions!)

Answer 1 would only be right if you were also asking the other person to take their own hand ('Let's do this together'), which doesn't make very good sense in this situation.
Answer 2 is the correct words to the song (which you might like to look up online, if you don't already know it)
Answer 3 is another way of doing it, but if you ask the 'Why? question, you may get an answer such as 'Because I don't want you to touch me' or 'In my country we could be arrested for walking hand-in-hand along a public road'!
Answer 4 is possible, but rather a formal way to make this friendly suggestion; and there are too many words to fit with the rhythm of the song.

'Pass' is the right verb, not 'give' (though that would be better than nothing; but then, you're not going to keep all of the salt forever, are you?). 'Send' is quite a good guess, but still not the right word.
Note that we say 'the salt', even though we only want a small part of it. We do not ask for 'some salt' unless, perhaps, we want someone sitting closer to it to just put a little on the side of our plate for us, without touching the salt-pot ourselves.

'Please ...!' is the best start, and the rest of Answer 2 will remind you how to give both negative and positive commands.

Answer 2 is clear and polite. You can also use this if someone approaches you in a way that makes you feel uncomfortable.