The actions and things you have to 心配 about are your cares and worries.
The reading is the reading of 心配 (which you've hopefully gotten down okay by now) and 事 using the (こと) reading. It is rendaku'd, as well, so beware of the ごと (just another 心配事, ammiright?).
Thank you for laughing my cares away.
Apparently he's got some worries.
My biggest worry is volcanic ash falling over the city.