My question is: can I just create a new receiving address in the read only part of the cold wallet which is online
A cold wallet is referred as “cold”, because it's disconnected from the internet. I guess that you consider it cold, because it's watch-only. Yeah, that may be true, there isn't a standard definition for “cold wallet”, anyway. To answer your question, yes you can create a new receiving address from the cold wallet, transfer it to the input field of the “hot electrum” and then broadcast that transaction.
And afterwards, how do I update the coins on my off-line machine So it shows the same amount of coins as on the read-only part?
Didn't you say that the “cold wallet” is online? If it is, it'll update your balance.