The cost issue should be your first warning. Due to the amount of fired brass readily available on the market, companies have sprung up all over reloading fired brass and selling the ammo. You really have to know who you're dealing with when buying ammo. You don't want to pay "new" ammo prices for someone's reload. Often, usually new shooters, make the mistake of trusting the headstamp to be an indication of who/when it was loaded. Any more, you'll find that's misleading more than helpful. Something like American Eagle black box, you know who made it when. If you're buying ammo with Joe Blow's Ammo logo on the box, or in a generic ammo can, etc., you have no idea whether it's factory, who loaded it, when etc. You need to learn the clues to indicating factory vs reloaded. Don't just look at the headstamp.
So, the cheaper ammo that you're referring to, could very well be someone's reloads, not factory ammo. Factory ammo should command a premium.
As pointed out, however, corrosive primed ammo, which would be factory loads (no one REloads with corrosive primers), is often cheaper than other ammo (factory or otherwise) simply because of it's corrosivity. Nothing inherently bad with corrosive ammo, you just need to know what to clean your rifle with afterwards and be DEDICATED to doing that cleaning same day as you shoot. Put it off and you're in for nasty expensive surprises. That cleaning challenge generally forces customers to pass over corrosive ammo for others and sellers have to drop the prices to move it.
If in doubt, get a good pic of the bullet/case neck area and the headstamp. Post them here or send them to someone here who's got the experience and we can tell, about 75% of the time what you're looking at. Get a photo of the packaging's markings too.
As to the AP bullet, it's only a theoretical advantage. Everything is relative. Compared the M33 Ball, M2 AP MIGHT have a slight accuracy advantage due to the lead base plug in the M33 Ball projectile. Those projectiles, especially if they've been pulled from ammo and reloaded into other ammo, can have a loosened lead base plug. When that plug comes out, wholly or partially, you have a sudden shift in bullet weight and balance which can make it a flyer compared to others you'd already fired or will fire. When M33 projos are pulled from ammo, it's done with a guillotine blade cutting a case neck or a tractor mechanism grabbing/pulling the bullet out. These will deform the projectile to varying degrees, making it more likely, not guaranteed, the lead base plug can be loosened and then come out when reloaded/fired. I've seen many M33 ball projos floating around for sale without the lead base plug. I've also seen M33 projos where the base was just a clump of white compressed powder. This is the lead base plug decomposinig. When fired, it'll disintegrate causing the same problem.
By comparison, the M2 AP has no base plug. The copper jacket is pulled down and wrapped around the base of the core. You can see the difference in the bullets easily with the naked eye. So the M2 AP isn't handicapped with the lead base plug design of the M33 and it's POTENTIAL issues when the projectiles are demilled/reloaded.
An awful lot of info to pass on here. The answers to those two questions of yours can be complex.