Humidifier
noun
An "add dampness container" is a container that adds dampness to the air. That's a humidifier.
かしつき
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
最近加湿器の調子が悪いんだよね。
Something has been wrong with my humidifier.