Chain & Sprocket wear

i think it doeas have some truth cos if the chain is worn the pins will have groves in them...

sooo....

when the chain goes around the un-worn chainring, the chain would be pushed together, thus making it possible to pull away, indicating chain wear.

True dat. chains don't stretch they wear down, if you got a pair of calipers (or ruler) you can check the chain at the pin points to see if it's gained length. 24 links is a foot. depends on who you speak to .5% or 1% gain is time for a new chain. Riding Fixed/Brakeless i would change yearly
I think Sheldon has some guides to measuring em

as for slipping, could be chainline, cog, chain. bit an elimination exercise is needed man