Exchange-traded options may be marked-to-market (I have no personal experience with them), but OTC options wouldn’t be unless there’s a specific provision in the agreement to mark to market.
Gamma is greatest when the option is close to expiration and the strike price is close to the spot price of the underlying: you’re very near the kink in the payoff graph, where the slope changes from 0 to +1 (for a call) or from -1 to 0 (for a put); a small price change from out-of-the-money to in-the-money (or vice versa) causes a jump in delta of nearly ±1.
I’m not sure what you mean by a swap’s gamma. Please elaborate on that.
For options, I think of gamma as “hurry up and get close to where you are going to end up anyway.” If the option is OTM, gamma will make it even more OTM, and similarly for ITM. That’s why you’re never sure where an ATM option is going to go and delta hedging is tough.