1. Will it for sure create a new address?
Yes, electrum will always be able to creates a new address. Electrum generates a seed from which tons of addresses can be made of.
2. Are all addresses created unique? For sure?
Addresses created are random. They are not unique "for sure". But the possibility of finding a private key, someone else already found are almost 0.
Meaning if every PC on this planet would create addresses 24/7.. there probably wouldnt be a collision until whole mankind dies. (Including Birthay paradox)
3. Do I have to hurry to put BTC into the offline created address, before anyone else gets it in a hot wallet?
Theoretically you dont have to worry. But the earlier its in your offline generated wallet.. the faster its in a "safe place".
If you are using Windows and you are browsing / reading mails on your PC.. its probably not a good idea to keep them in a normal wallet on your desktop.