On this course It is never allowed to drop 'there' from 'there is', even though it is perfectly correct (except at the start of a clause). Please report it wherever you can find it. This issue affects many questions.
The usage of the instrumental case is not limited to showing the instrument of an action (this is only its main purpose). Here, it is used because the preposition под requires the following noun to be in the instrumental case.
I definitely hear стулом. If you still hear столом, try some "minimal pairs" training. Go to Forvo or Google Translate and play the audio for столом and стулом back to back until they start to sound different to you.