The market is an auction and its participants determine the price of the security. If they are actively offering better prices, the bid and the ask narrow. If not, they widen to wherever the market maker sets them. So from strike price to strike price, there will be minor deviations.
In addition, there will be minor deviations in the value of the SPY and the SPX options because the participants may be in one underlying and not the other as well as differences in liquidity, hence, the ratio will never be exactly the same.
I'm not sure what you are asking in your second question in regard to the real time price of options. The market sets the price based on the auction. The only option pricing formula calculation that you would make at that point would be to determine the implied volatility. A good broker provides that information in its option chains.
Perhaps you might want to determine what you think the fair price of an option is given your belief that the volatility should be higher or lower but that has nothing to do with market price. You'd need a calculator or software to do that and I suspect that's not what you're after.