How could I getting a good sleep

Are you asking how you can get a better nights sleep? I think the answers are in your post. Change the mattress, or sleep in a different bed. Ask your neighbour to be quiet. If he/she doesn’t comply, you can take recordings of the noise, and contact your council. Your backache may be related to something else, and not the mattress. See your GP.

I should change a firm mattress, and the noise from the neighbor by their problem, they often argue with each other. I may talk about with them. But I couldn't meet them because of they all back in every deep night.

I don’t understand your last sentence ?

You can make your side of the double bed harder by putting a large piece of hardboard under you, above the mattress, You then add soft foam to make it as soft or hard as you like.

This way you need not buy a new bed or a new mattress.

See doctor about backache as soon as you can as it may be nothing to do with your bed.