Question: Let's say I have 10 miners node in my network. Once a transaction is initiated, all nodes will be informed about this and then they start mining. 1st node has highest computational power and finished mining the block before other nodes do.
Now, will other nodes continue to mine the same block or they will stop mining after 1 st node has finished mining.

Answer: 
Actually, in Remix there's an "Account" dropdown right beneath "Environment" (where you select Javascript VM). It provides five test accounts for you.
You could create locally a blockchain with 10 test accounts using "[testrpc](https://github.com/ethereumjs/testrpc)", a fast Ethereum RPC client for testing and development. 

1. Download and install testrpc and then run on terminal "test-rpc". You will then have the 10 accounts and their private keys.
2. In Remix choose Web3-provider and connect to localhost:8545, where your test-rpc runs.