If someone asks you “lean in”, they are asking you to move your head closer so that you can hear what they have to say. It could be because you are in a loud place, or that someone wants to tell you something that they don’t want anyone else to hear.

No. 'Cut in line' in your text means to queue jump. There are people waiting to be served at the bar - a line of people in a queue. There may not be an actual line of people - just people waiting to be served in the order they came. Someone cutting in line is someone not going to the end of this line/queue to wait their turn. They don't wait their turn - they 'cut in line'.

Thanks all of you.

Definitely not

No, I've never heard this term used that way in English