Re: How somebody can prove that my wallet belong to him?
What if i catched some mot****er, who is using one of my wallets - how can i prove that it's mine? 
Most probably by the time you'll realize somebody is using your wallet, your funds will be gone. So you won't have to prove anything.
A person who knows the private key or wallet.dat + password owns the coins. There is not other way if the wallet is non-custodial.