I am quite new to Ethereum development . I would like to know if i can create new smart contracts using solidity programming language and deploy them to the network using Jaxx wallet . Right now I have downloaded Ethereum wallet from github for this purpose , but it takes a long time as it downloads all the blocks
No. You can only transfer crypto currency with Jaxx wallet. Although myetherwallet provides a function to deploy contracts without syncing all the node data.
MyEtherWallet doesn't compile the contract code for you. It takes in the byte code for contract deployment. You can use Remix for getting the bytecode of your contract.