Is there any way to simulate buy an option at a pric of x when that price is not available to buy ? If x-3 and x+3 exists, how do I buy it at price x?
With option pricing, at least with BSM model, you can observe every input except for implied volatility. So all you need to do is provide an implied volatility into your pricing model and your custom strike price to produce an option price. With that IV assumption, you can produce all the greeks you need according to BSM model.
If X-3 and X+3 are not that far from X (you'll have to use your judgement), you can expect that the IV of X to be in between the other two. IV also tends to be in between the two if X-3 and X+3 are at one end of the skew. Note that in practice, there may be cases where the IV of the middle option is not in between the two outer options, especially when you get close to ATM. However, the amount the IV of the middle option differs from the outer options has a bound (it cannot be so where the middle option is worth less or greater than both the outside options, with negligible adjustment for interest rates). Even if skew exists, you can still back into an approximate option price as long as you can supply an IV figure.
All the above is under the assumption you are talking about plain vanilla options and options on stuff like equity or commodity futures.