How can I check everything is fine with a cold wallet (offline Electrum)? I checked the addresses from the wallet on the blockchain and the funds don't match with the balance on the wallet...
I just want to point out that your statements are a bit contradictory here. If your wallet is a cold wallet/offline storage then it must not show you any kind of balance for your to compare. A cold wallet is a wallet that has never been and will never be connected to the internet. If it is otherwise (like being connected to the internet at some point in the past before you cut the internet off) then it can not be considered a cold storage.