Gas is purchased using Ether, does that mean I can send gas as a separate coin?
No, you can't send gas to an address, but you can send the equivalent amount in Ether.
Why? Gas does not exist as an own token but is merely a unit of accounting to attach a price to a specific operation in the Ethereum network. For example, the Ethereum Virtual Machine Opcode ADD consumes 3 gas.
How? You can estimate how much gas a transaction requires with the estimate gas API. The default gas price is currently 10 Szabo (May 2016). You can set your own Gas price, but Miners are free to ignore transactions whose gas price is too low.
Gas is not a token or a cryptocurrency. It is the most granular unit of payment for deploying and executing code in Ethereum. Currently conversion of ether to gas happens at the point where transaction (simple ether transfer or call to a contract) is included into a block (mined). Creator of a transaction offers a certain exchange ratio of ether to gas (this offer is written into the transaction as 'gas price'), and the miner accepts that offer by including transaction into the block.