1. Will it for sure create a new address?
The way Electrum works is that the seed will be able to create a lot of address, likely larger than you will ever need. With each transaction, Electrum lists the used address as used and never display it again, though you can still send Bitcoins to it. Electrum will then be displaying an unused address from its keypool for you to use.
2. Are all addresses created unique? For sure?
Yes.
3. Do I have to hurry to put BTC into the offline created address, before anyone else gets it in a hot wallet?
If you have a malware in your online computer, whatever you do, you'll never win against it. If you are receiving a large amount of Bitcoins, just send it directly to your cold storage and send some out again to spend it on your online wallet.