Chain & Sprocket wear

To JWB's question, side to side motion is not relevant on a bike chain (or on a motorbike either).

As others have said, measure length increase and replace earlier rather than later. Clean clean clean and lubricatee (though that's another whole story in itself)

regular cleaning tends to get shot of annoying crunchiness in a chain - while removing and soaking in surgical spirits is a neccessary pain in the arse every so often, a quick wipe of the chain and chainring with some household citrus wipes tends to do the trick nicely in the short term. s'long as you dont have any misgivings about creating landfill.