What is the average lifespan of a phono cartridge?

Tough question. a lot of variables.
In general cart makers usually say 1,000 hours of play time.
That can vary. If you play 'dirty' records with a lot of snap crackle and pop your stylus is going to wear faster.
If you play perfect clean Lps and use a stylus preservative like Stylast your stylus is going to last longer.
I would say 2,000 hours is a reasonable life for a stylus if you use Stylast faithfully.

And how does anyone "know" how many hours they really played?
It is total guessing on most folks part. Unless one uses some sort of device to keep track, it is just a wild guess every time. (usually below the real time used, more often than not, half the real time IMO)

I use a mechanical clicker to count each LP side played. Then I average the sides out to 20 minutes. So 3,000 clicks is 1,000 hours. that is the best i can do.

I have a 27 year old Dynavector Ruby 23 which i still use on a spare TT, The original owner used Stylast faithfully, and he gave me the cart. I would have to guess the cart has around a thousand hours.. but it is fine.

To really know if a stylus is worn you need to use a magnifying device and actually look at the stylus.
Used to be many good HiFi stores had a microscope just for looking at the stylus. Not anymore. Same thing most stores now cannot really mount a cartridge with any sort of accuracy.

Anyway, buying a used cart is 100% trusting the seller. If you believe the seller....

Hard to say, because there are differences from Manufacturer to Manufacturer.
I had a - heavy - Takeda Miyabi which was still strong after 8 years or regular
use (a few times per week), had a Shelter which was down after 1.5 years.

you don't see it as a red flag that used cartridges were always used for about "200 hours?" Many here will buy just about anything used, except a cartridge.

New phono cartridge is almost like new guitar strings. Unfortunately longer service makes sound more dull. In most cases I tend to keep it for 600 hours before purchasing or trading in to a new one.

There are a lot of variable involved. Cheaper cartridges use synthetic diamonds that don't last nearly as long as premium styli that are carefully cut and mounted so that the crystal structure is oriented properly to minimize wear.

How the user handles records and cartridges will also matter. If records and styli are kept clean, they last longer. According to one manufacturer (Benz or VdH, styli can last as long as 2,500 hours if the records are kept clean). I've used Lyra cartridges for close to 2,000 hours with no problems or sign of deterioration in tracking ability.

The rubber suspension parts of cartridges can go bad from aging and exposure to environmental agents (primarily ozone). So, even if unused, a cartridge could go bad. That is the theory, but, I've personally never encountered such problems--I've heard very old cartridges that still sound good after long storage.

My way of determining when a cartridge is beginning to go bad is to find the very few records that are challenging to track properly and listening for changes in the ability to handle the very few spots where distortion can be heard when everything is less than optimal.