Is the Darkness invincible or not? The comic seems to jump back and forth on that point constantly. In the very first comic the Angelus seems convinced that killing Jackie before his 21st birthday will finish off the Darkness for good, but later it's shown that Jackie's grandmother was gunned down while pregnant with his father, and the Darkness simply turned her immortal easy as that. Then in a later story, Jackie is shot during daylight, and the Darkness can't seem to do a thing to help him except have the Darklings drag him off to a surgeon - fine, except one of the flash-forward stories has a Darkness host killed by daylight and then simply pieced back together fine and dandy in the next panel. Finally, when Jackie actually does get killed and endures a brief stay in hell, the Darkness simply rebuilds his body. So what's the deal? Is each Darkness host simply impossible to keep dead until getting a woman pregnant?
The Darkness has yet to be defeated. If it hasn't passed on to a successor yet, it will do everything it can to bring the current holder back to life. The Angelus believes there has to be a limit to this power, and tries to kill its host whenever it can.
In the game, the police ambush Jackie at a church where he has agreed to meet Eddie Shrote. They cut the lights before piling in wearing full SWAT gear. Of course Jackie's powers being fuelled by darkness, they get slaughtered. Until halfway through the fight, where Eddie suddenly calls out "hit the floodlights, he can't do that shit in the light!". So if Eddie knew Jackie's weakness, why'd he cut the lights in the first place? Yes, he might have only figured it out during the fight by watching how Jackie either avoided it, or shot out all light sources. But during the church fight, all the lights have already been cut, so there's no light for Jackie to avoid. Eddie was more likely to have guessed Jackie's weakness during the other few times he see's Jackie in action (such as when Jackie chased him through his own police station, a set-piece where, if the player is smart, he'll shoot out every light he comes across). So what, did Eddie just think it'd be funny to feed some of his few remaining SWAT personnel (Jackie having slaughtered more than half the force at this point) to the Eldritch Abomination empowered Hitman Witha Heart?
Schrote sent the few remaining "good cops" in first?
Combined with the above, he was testing a theory? I'm going to assume that the player, at that point, cut loose with every power they had, and an observer would quickly see that Jackie wasn't just destroying lights for effect, he was actually weakened by the light. Personally, I would switch off Darkness Mode whenever surrounded by too many light sources to avoid draining too much power, it's not too much of a stretch to assume canon!Jackie does the same thing.
If Jackie will die if he impregnates a woman, why doesn't he just try using a condom?
This is brought up right off the bat in the comics, when he finds out he just says he'd use Birth Control, only to be countered that no birth control is 100% effective. Condoms break, the pill fails, and Jackie gets the life sucked out of him.
There are women out there who have had hysterectomies, and that's certainly a 100% guarantee that impregnation won't happen. I'm not up on the comics, has this point been brought up at all?
Why doesn't Jackie just have a vasectomy? Or would the Darkness repair that as if it were an injury?
Bingo. The Darkness would regard a vasectomy as an injury and "fix" it.
Not to mention that The Darkness wants to be the one in control of Jackie and not vice-versa. Apart of that is having the option to just go to the next host. They flipped-flopped on wether or not the current Darkness user dies at the moment of conception (as it was initially), at the moment of birth or merely that they lose their powers at the moment of birth (as seen in the lastest issue I've read, which is several years old by this point). In that last example, Jackie's father keeps his Darkness powers up until Jackie is born, at which point he's killed by the people he was attacking just a moment before.