You bite off heads by aiming directly at them at comparably low range - when the aiming is right, teeth appear at the edges of the screen. Just left click while the teeth are visible and you perform a bite. It's pretty hard to pull off with moving targets (although you can get pretty good at it with practice) but it's easy to do on static enemies. There's a fair amount occasions where you can hang above an unaware enemy on the ceiling and bite their head off from there. It's quite easy to do on cowering civilians so make sure you don't just scratch those to death. Sadly you can't. When you catch fire the key is to quickly replenish lots of health by biting off heads and scratching away at dead bodies. I've managed quite a few times to have almost full health when a fire goes out by simply replenishing health quickly enough while burning. I assure you that throughout most of the Marine campaign there's infinitely spawning aliens (and from what I recall in certain sections of the Predator campaign as well). It's just in the very beginning of the Marine campaign that all alien spawns are scripted.

And no, you misunderstood me. There is no formal time limit. It's just that you have limited resources per level (ammo, healthpacks) in contrast to endless enemies. It means that if you don't get the job done quickly enough you will inevitably run out of health and/or ammo - that's what I referred to as "basically a time limit". Obviously can survive longer if you're really good.

The other characters' difference is this:
1. The Predator regenerates (albeit slowly) that blue energy which powers the shoulder cannon as well as that defibrilator healing thingy. He can always heal himself if he waits long enough. Additionally the Predator has a variety of useful attacks that do not require ammo. Even his wristblade is powerful (especially it's secondary attack) and eventually he gets a throwable disc that returns to him like a boomerang - only recalling the disc, e.g. if it gets lost, requires a bit of energy. His only weapon for which there's limited ammo per level is that harpoon gun or whatever it was called.
2. The Alien does have limited health, however, unlike the other characters the Alien never encounters infinitely spawning enemies since it's only aliens that spawn infinitely and you don't fight those as an alien yourself. And even if there were infinitely spawning enemies (there might be some rare sections with infinitely spawning humans but I don't think so): more enemies would also mean more health since biting and scratching organic enemies heals the alien. So as long as you - on average - manage to replenish more health per encounter than you lose, you're good. And obviously the Alien does not need any ammo.

It's only the Marine who has to deal with strictly limited health and ammo. In Aliens versus Predator 2 the levels are more linear and all enemy spawns are scripted - there's none of the endlessly spawning aliens there and you will rarely (if ever) run aimlessly around while getting overrun by enemies. And generally the balancing is more forgiving there. It's simply a more traditional and polished story-driven FPS than the first Aliens versus Predator is. I think it also has unlimited quick saves by default. AvP 2, unlike the first one, never gave me a hard time.

Personally I like AvP 2 less for exactly these reasons, because it's a more typical story-driven FPS while I love the original game for how original and even experimental it is. However, if you just want a good FPS in the Alien franchise AvP 2 should be right up your alley. I haven't played AvP 2 in almost ten years but from what I recall it has generally aged pretty well.

Also, there's really no story-reasons to finish the first game before going for the second. AvP 2 is not as much a sequel as it is just another game in the same franchise (it was also made by a different studio, namely Monolith who also made No One Lives Forever and F.E.A.R., among others). So if you're not enjoying AvP Classic 2000 at all I recommend you just go for AvP 2 right away.