I've noticed that some zombies tend to stay down, while others keep rising a bunch of times before giving up (temporarily?). So barring an exploding head, do they keep doing that with varying intervals? Is there a way to make sure they don't?
Do zombies always get up eventually?
No. Once a zombie is dead, it's dead. What you're experiencing is a "knockdown" mechanic, where zombies will fall over after taking so much damage. This feature was present in other games in the series as well, and the amount of damage required was random (just like zombie HP), and the same appears to be true for the RE2 remake as well. When a zombie gets knocked down in this way, it'll eventually get back up again (unless you destroy it's legs, but then it'll just crawl around instead). If the zombie is really dead though, then it's never getting back up. You can test if a zombie is really dead by attacking it again, either with a knife or a weapon (although I suggest using a knife).
Destroying a zombies head will instantly kill it, so there's no need to check. In the older games (or at least the RE1 remake) destroying a zombies head was the result of getting a "critical hit", which was a hidden modifier all the weapons had. Based on my experience I'm positive the same is true for headshots in this game, but I can't be certain.
Finally, there's fire damage. Fire is really effective at killing zombies, and just the undead in general. Outside of the massive damage it does, though, there's nothing special about fire damage in Resident Evil 2. There is a cutscene and some notes about how you need to burn them to kill them for good, but I think this is just to give a hint to the player that fire is really effective at killing zombies. It's also possible that it's meant as a reference to the Resident Evil 1 remake, where zombies turned into crimson heads if you didn't burn them.
From what I experienced so far, zombies won't get up:
- if you shoot their heads off obviously;
- if you shoot their legs (crawling zombies are still dangerous, but at least move slowly).
Also, once they are on the ground you can do few attacks with knife to check if they are pacified for now.
I've also seen mentions that some powerful weapon somewhere later in the game can destroy zombies completely. This weapon is :
Since the game is new and not much guides are available yet, I cannot back this up with sources.