You can not change the gas price of EVM instructions without hacking the core and totally forking off to a new client. This is true for both Geth and Parity.
If the gas limits are not sufficient for you, you can just increase the following configuration options for Parity:
--gas-floor-target GAS Amount of gas per block to target when sealing a new
block (default: 4700000).
--gas-cap GAS A cap on how large we will raise the gas limit per
block due to transaction volume (default: 6283184).
You could try to start with a floor of around 9999999 and a cap of 99999999. And see if this works out for you. Now we covered the limits.
If you want to override gas prices to be accepted by miners, you have to change the following parameter:
--gasprice WEI Minimum amount of Wei per GAS to be paid for a
transaction to be accepted for mining. Overrides
You could try to set it as low as 1 Wei.
And to cover your last question: You can not specify gas price in a genesis block.