My question is: can I just create a new receiving address in the read only part of the cold wallet which is online and then sent my coins to that address from the hot wallet?
Yes. Provided you are certain that your watch only wallet is indeed showing the same addresses as your main cold wallet, which will be the case if you exported the master public key from your cold wallet as you should have done, then any addresses you generate on your watch only wallet will also be generated in the same order by your main cold wallet.
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?
You generally don't. You only need to see an up-to-date balance on the watch only wallet. You use the watch only wallet to create an unsigned transaction, and then move that unsigned transaction to your offline cold wallet to be signed. The offline cold wallet does not need to know the up-to-date balance on the addresses in it. As long as it has the private keys, it will sign the transactions without any issue.