It can be, when it is a direction. An example is "we went up in a balloon."
It can also be an adjective or preposition (up the tree), and colloquially a noun or verb.
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No, it is not an adverb. The word tree is a noun, or verb (to chase up a tree). The adjective is "treed" (active or passive) but there is no adverb form.
She jumped high up into the air. The word "high" is an adverb in the sentence above.
No. The words up and upon are prepositions, but upwards is an adverb. It cannot be a preposition.
Does is a verb, not an adverb.
The adverb is highly