Learn Russian: Каждый день я вытираю пыль со стола.

It is added to make pronunciation easier! When the preposition с comes right before certain consonant clusters, especially those starting with с or з (like the ст- in стола), an о is added. Trying to say с стола would create an awkward double-s sound, so Russian uses со стола instead.

Why do we use со to mean 'off of' instead of из (from/out of)?

In Russian, prepositions of motion are strictly paired with prepositions of location. Dust sits on the surface of the table (на столе). The grammatical counterpart to на (on) is с or со (off/from). If you were taking something out from inside a desk drawer (в столе), you would use the counterpart to в, which is из (out of).

Пыль (dust) is a feminine noun, so why doesn't its ending change to -у or -ю since it is the direct object?

You are right that it is in the accusative case because it is the direct object being wiped. However, feminine nouns that end in a soft sign (-ь) in their dictionary form, like пыль or ночь, belong to the 3rd declension and do not change their endings in the accusative case. They look exactly like their nominative forms.