[BetterThings2]

where did you order from?

Seller = Amazon
Delivred by amazon

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I sent them the proof of deposit at the recycling center, now they no longer want to refund me without return. They tell me to contact apple and see directly with them. What are your solutions?

Amazon is clearly playing games with you.  If they truly said that they can't refund without proof of deposit, and when you sent them the proof now they want to say they can't help you...is unnacceptable on their part.  I would Phone Amz and tell them per their own words they said they would refund me when I sent them the proof they asked for.  I would hammer that point home, and let them know that you don't appreciate them moving goal posts.

I will try that way, if it fail, i will try dry ice method

If i use dry ice, do you know how much in need to put in for a travel of 2-3 days ?

The box weight is 7.7 lbs
Thooses days are cold like 59.0 °F (15C°)

For a little reference 5lbs of dry ice takes about 24hrs to fully sublimate (turn to gas) 7.7lbs of dry ice would be a lot of ice, plus you say it's pretty cold where you are at so that would slow down the sublimation process.