Questions on Electrum wallet and setting up ofline

[Randomhero360]

First, can I set up an electrum wallet offline? or do I have to set up a cold storage wallet while my machine is connected to the internet? Second, when I send coins to that address how does it get to my wallet?

My understanding is the coins just get tethered to the wallet address in "cyber space" and never actually gets to the wallet, but my private key allows me access to them once I want them and connected to the blockchain. Is this correct?

Also when I create a wallet online, say with MEW, how does the blockchain know it is an address if the machines and wallet never connects? or is it simply the transaction file it reads and sends it to whatever address is says whether it's valid or not?