Jim IS correct concerning putts, but there are a few exceptions:
- putts from fringe DO count, while putts on the green are "free". That is what you may have encountered.
- Mulligans DO count as 2 on the green,
- putting CTTH may count, IIRC.
Also, the shot to the green may be the last in a ball's life, so it may disappear before the first putt.
Ball life has been counted to be between 90 and 125 hits (durability 1 to 2.5) in 2012(?), I don't know about newer types like MAX...
I used to think that a sleeve (durability 2) lasts for 10 nine hole rounds, but that was as a TP or Master, so it may be more with lower scores.
But, don't expect a useful WGT answer on product characteristics here, much less to your email. You'd have to write to CS ("Contact" below) and hope for a reply.