It's gonna be a normal transaction anyway, whether it is to send to an ICO or not.
Hence the transaction needs to have more than 1 ETH in your wallet, the additional is the transaction cost.
If I send 1ETH to the contract address, will it fail for insufficient
fee amount ?
Yes, it's going to fail because you don't have enough to pay the transaction fee.
How much do I need to have in my wallet to send 1 ETH to the contract
address ? Is it ( 1ETH + transaction Fee i.e, Gas) ?
Yes, it'll be 1 ETH + transaction fee and the transaction fee depends on the gas price you select.
What happen when transaction fails ? the (transaction amount +
transaction Fee ) will be returned back ?
If you face a Out Of Gas Error, the transaction amount will be rolled back, but not the transaction fee. Transaction fee until the execution got failed will be charged anyway. Referring to this question will also be useful.