EDIT:
If I import a key from an offline wallet into an online one, do my transactions and send the rest of the balance into an another address of the same offline wallet, can it still be compromised?
The terms "offline" and "online" are a bit confusing. I am not sure what you are asking...
After i have used all the addresses and private keys of the offline wallet, can I make add more into it or should I just make another offline wallet?
I am assuming you are speaking of an Electrum wallet...
The wallet software will keep generating new addresses. If it is a more extreme usecase (>10,000 TX total) then it might be worth creating a new wallet. Again, not sure what you mean by "offline"
When I make an offline wallet, are the keys password protected? do I have to provide the password when importing a key from another wallet??
Thanks
Again, define offline wallet.
Personally, an online wallet is synonymous to a web wallet service (blockchain, coinkite, etc.)