Do the exchanges provide your own independent addresses for use?
Pretty much.
Incoming only though. You can't sign using the address, and you can't send from that address. It'll come out of a random address, so don't try to play any dice games with one.
Is there a Litecoin Web Based or Light Client similar to blockchain.info or Electrum/Armory so that Litecoin can be used without downloading whole blockchain?
https://www.coinwallet.coThis is a horrible idea. As we've seen with instawallet, MyBitcoin, inputs.io and a variety of other services...
YOU CANNOT TRUST HOSTED WALLET SERVICESUnless it's an in-browser managed wallet like blockchain, where the service doesn't get your private keys, then it's not safe.
The next safest place is in an exchange such as BTC-e.
Either way, the Litecoin blockchain is only around 4gb, compared to Bitcoin's 16gb+ blockhain, so you might be best just using the real client.