Some report getting more mileage than you've gone and not having any problems.

Most people notice they have a worn chain when it starts to skip, usually under heavier pedaling.

Replacing the chain when worn will save the sprockets and chainrings although the chainrings (in front) are usually the last to wear.

The conventional way to measure chain wear is to measure the distance between 25 pins while the chain is stretched out. A new chain should be exactly 12" long because each link is 1/2". A stretched (actually, it's wear, not stretch) chain will be longer. IIRC you don't want it stretching more than 1/8".

Keeping a chain clean seems to help some but others swear it's enough to oil each roller and then wipe off the excess oil because the oil takes a path that supposedly flushes fine grit out to the sideplates when you oil the roller. (except with really old chains on vintage bikes because they're put together different.)