Who can analyze the condition of my old cartridge?

You can easily do it yourself with a low powered "toy" microscope or stereoscope. Look at the shape and wear of the stylus tip. Look at whether the cantilver is straight. Look at whether the stylus surround is compliant (i.e. not hard) and whether it is cracked. For an MC cartridge, any further inspection would involve looking at the wires which would probably involve taking it apart as in a retipping. The cost of having somebody do this is probably not worth it unless you are actually doing a retipping.

You really can't, without risking destructive testing. After a cartridge is older then ten years, the rubber is shot. Stylus wear is easy to look at, but the tip and shank connection is another crap shoot. Best to sell the lot on ebay, as is.

Thanks for the feedback.

The stylus looks good on each cartridge, but don't know how to look for or evaluate wear.

As for the rubber bits, I can look for cracks, but how do you decide if there is a hardening of the rubber?

If the rubber is cracked, it is definitely hardened. However, before actual cracking happens, you can notice subtle changes. When rubber dries out, the surface tends to get a glossy sheen to it. It's sort of like the "skin" that forms on top of a bowl of pudding that's been sitting for a few hours. On the other hand, some rubbers are made to have a glossy, hard surface, a hockey puck for example, so that's not definitive. You need to have a point of comparison, for example, a new stylus/cartridge that you can visually compare the old one too. Of course, there's always your ears. Does the cartridge still sound okay or do you notice a deterioration in performance.

I don't think you need to make this too complicated for yourself. If the cartridge/stylus looks fine, i.e. the tip is not worn out of shape, if the cantilever is straight, if there are no cracks in the surround, then that's as far as you need to go. After that, just be honest in your for sale ad. Say how old the cartridge is, how much use it has and price accordingly. Wear and tear from depreciation is taken into account in pricing used goods. It's up to the buyer to satisfy himself that the price is appropriate for the condition of the item. He just needs to know that the item is accurately described when put up for sale.

"You really can't, without risking destructive testing. After a cartridge is older then ten years, the rubber is shot." Tell that to my 20+ yr old cartridges that still perform perfectly.
Those usb microscopes work great. check out VE nude pictures