Does anyone know

if it is legal to operate a golf cart in Ajijic? Getting old & having trouble walking.  

no

I only know they are to never be on the Carretera.

It's risky to buy one as the powers-that-be are currently not enforcing their illegality, at least below the carretera.  A change in their position, or a new administration could clamp down on them as had happened in the past.

If you do get one, make sure it has Jalisco plates and is fully insured--from what I hear both these tasks are now nearly impossible for new registrations.

The main problem is that they cannot be insured for liability which is mandatory for any car or motorcycle over 150 CC on any public road in Mexico. Yes, the transitos turn a blind eye to golf carts and ATV's however, as stated above, they could change their minds. If for some reason you injure someone or cause serious damage you will be in jail until reparations have been made since there is no liability insurance......

As stated above, they are not legal but only tolerated — for now. They can become no longer tolerated without notice.
There was a small group of Ajijic women who lobbied the then administration for the carts. They worked out the current deal of toleration with license and insurance. That was okay when there about six of them. Then newcomers decided they were legal and they wanted one also. Newer-comers decided Ajijic was some sort of resort where golf carts were not tolerated but welcomed.
It is only a matter of time until “something” will happen and, POOF, suddenly you won’t be able to use the cart anymore and who you going to sell it to?

What do they cost?

New ones can cost over 10K USD. A decent used one would probably be around $5K USD. The cobblestones take their toll on these pretty fast.

Yes, suspension-wise they are meant to ride along..... golf course fairways which are generally silky smooth! Cobblestones.... not so much.