I tried sending 0.0001 BTC from my blockchain.info wallet. It deducted 0.0009 BTC from my account, including a 0.0008 BTC is transaction fee.
Is it correct that the transaction fee is 8 times larger than the amount sent?
That's the recommended fee, the recommended fee is like the minimum amount to get your transaction included in a block ASAP. You should be able to set fees, but for small amounts like that a fee that large is common, remember, miners can only include so many transactions a block every 10 minutes, so they pick the transactions with the largest fee and smallest txn size.
The details about bitcoin fees are explained here. In short: If you don't pay fees for small amounts, it takes longer until your transactions are included in a block and thus confirmed (to avoid "dust" spam). For blockchain.info you can click on "Send Money" and then "custom" to specify 0 BTC for "Miners Fee". I don't see a problem with this, because they get 25 BTC anyway for mining a block.