You're welcome, glad it's helpful!

...a buddy of mine who's had some hazmat training says that the filters have a finite life once they're opened because some of the materials in them are highly reactive to neutralize the worst of the warfare environmental nasties. As a result, I keep a couple new filters sealed up and squirreled away just in case I need it for it's proper purpose.
They have expiration dates on them, too, but he was less concerned about the expiration dates than the number of months they'd been opened. He said anything past 60-90 days and he wouldn't trust his life to it.
Yes, once a package is opened the cartridges will set to work whether or not you actually use them, the only difference is that without air being forced directly through them it takes longer for them to get "used up" so to speak. You should be able to extend the opened shelf life of the cartridges by placing them in ziplock bags when not in use.
As far as trusting your life to it goes, the respirators I use specifically state that they are "
Not for use in environments that are immediately dangerous to life and health". Rather, they offer protection "up to 10 times the Permissible Exposure Limit". In my current use of them I am often entrusting my life to them due to some significant health problems. My personal comfort level is if I'm expecting a chemical exposure that may be unusually strong then I generally won't go into it with cartridges over a month out of the packaging, and only then after I have worn them and determined by feel that they should be acceptable. If I have any doubt I can always take along an unopened package of cartridges just in case, though I've only done so once and have not found myself in need of it to date.
2. How long can we expect those cartridges to last in actual use? How would one know when to change them?
Some cartridges come equipped with a passive "End of Service Life" indicator, or "ESLI"s, however this may or may not be accurate as far as actual safety in use. The organic vapor cartridges I've seen do not have ELSIs.
How long they last in actual use will depend on how long they're worn for, humidity levels, and the concentrations of chemicals in the air at the time. So it's pretty subjective. I've only just now begun keeping records of how long mine last, but taking a rough estimate of what I've gone through I'd guess that I switch them out about once every 10 weeks, and that would be wearing it on average 4 - 8 hours a week in normal everyday environments and taking no special precautions to preserve the cartridges when not in use. When I remove the cartridges from my mask they still have a fair amount of potential use left, and I keep them on hand as singular backups until they're rotated to the trash when the next pair takes their spot.
"Singular backups" is just my term for breathing through a single cartridge sans mask, a little trick I picked up out of necessity once. It requires strict inhalation through the mouth only and an airtight connection of mouth to cartridge opening. I sometimes use this method when the air is okay enough that some accidental exposure would not be harmful. It's much less obtrusive than the mask, particularly for conversations or EDC, and is also used to bridge the gap if it turns out my mask is needed after all.
For the mask, as the time draws near to change them I notice inhalation requiring more effort, and the resulting air feels "muggy". Sometimes if I really stretch out a wearing I'll begin to smell the faintest traces of chemicals when I'm in an environment particularly heavy with them, but usually not. Usually the sensation becomes more and more obvious until I swap them out purely for comfort reasons, and I'm immediately rewarded by the notably fresher, easier air I get with the new ones in. Granted this indication requires some experience until you can be confident you recognize it, but the worst that happens is you needlessly open a new package, swap them, and notice no difference, at which point you can just place a pair in a ziplock bag and try it again later.
For my singular backups, if I inhale through them and they make me cough, I throw them away.

But so far that's only happened when I've been lazy about rotating and I have ones that have been sitting in the open air for like 5 months after being used in my mask. Dust alone could probably account for that.
Which brings me to another note: chemical cartridges and particulate filters are two different things; each can be used in the mask individually or they can be combined either manually or packaged into a single unit at the factory. Some filters even provide nuisance vapor protection, but the job of filters is to trap particles; the job of cartridges is to adsorb and/or react with chemicals. Make sure you use the right item for the job. I rarely encounter high particulate situations but I want to make sure that if I ever do my mask won't be clogged by them. So I've opted to manually add filters to my cartridges, that way so long as the filters stay clean I can keep reusing them as I swap out the cartridges. If the reverse were true I could swap out the filters while keeping the same cartridges. I like the flexibility and the replacement filters are cheap, thin, and lightweight so it's little trouble to have them around.
1. In general, I know gas masks will protect a person from many substances but there are some things it is not designed to filter out. What will a gas mask stop and what will get through a gas mask?
That will depend on which cartridges are in the mask. I use the most basic cartridges, which are termed "organic vapor" and will generally take care of anything you throw at it with the following technical exceptions: formaldehyde, ammonia, mercury vapor, and acid gasses such as chlorine, chloride, and sulfur dioxide. I say "technical" because these are specs for work environments, so it's not like there is zero protection otherwise. I've walked by freshly ammonia covered windows and a chlorinated swimming pool without smelling either; it's just a matter of the protection cannot be guaranteed and doesn't last nearly as long as when the cartridge is designed to handle it.
Organic vapor cartridges use activated carbon to adsorb the chemicals, whereas the other cartridges rely on very specific chemical reactions to take place that neutralize the targeted chemicals. Some cartridges will protect from both organic vapors and one or more targeted gases - read the label to see which specific ones are included. I've never had need for the more highly specialized cartridges; if you're looking for the widest net to throw as far as covering the most chemicals at once the organic vapor/acid gas combo is probably it. I personally found that in my exposures I didn't have a need for it, and switched back when I noticed no difference.
This page is an excellent resource for info on chemical cartridges, and I used it to back up some of the above info.
3. What can we expect to pay on average and where is the best place to get one?
The best place to get one is in person from a safety supply store. Most of their customers tend to be big companies that do their business over the phone or computer so they're often really happy to work with someone face to face and in our experience will often give a discount just 'cause you're there. If you call in and talk about what you're looking for and why, and presently ask for a discount, it's likely you'll get one.
I tend to pay about $10 a mask and $9 per cartridge pair, or less depending on further discounts.