Can I replay heist missions in GTA V single player?

You can replay Heist missions using the Replay feature. However, doing so will not influence the rest of the game. You can neither improve your finances nor your crew by replaying Heists or any other missions.

Navigate the start menu, and you can replay a mission. When you choose to do so, the game will notify you that it creates a save state of your current progress, allows you replay the past mission, and then restores that save state once the mission is completed.

You can't gain additional money, or level up your crew as nothing is saved from replaying missions. You can, however, do the heists the second way (as most of them give you two approaches) to attempt the gold medal objectives, which will save if you achieve them.

Replaying missions has no influential ability on the game, anything you gain will be lost. It's just to improve if you feel you need to.

My friend tried to get into a rare car at the end of a mission, thinking he could drive away. Instead the screen faded and it loads back to the original game...