Your answers mostly seem correct. Here are the corrections:
1/ The prepositional phrase is "of bones and ivory tusks", and it modifies the word "display". The correct abbreviation would be ADJ, as it is an adjective phrase modifying the noun "display".
2/ The prepositional phrases are "for visitors" and "to touch", and they both modify the word "tusk". The correct abbreviation would be ADJ, as they are adjective phrases modifying the noun "tusk".
3/ The prepositional phrase is "on a poster", and it modifies the word "map". The correct abbreviation would be ADJ, as it is an adjective phrase modifying the noun "map". The prepositional phrase "of famous mammoth fossils" modifies the word "sites", and the correct abbreviation would be ADJ.
4/ The prepositional phrase is "of all the science fair projects", and it modifies the word "informative". The correct abbreviation would be ADJ, as it is an adjective phrase modifying the adjective "informative".
5/ The prepositional phrase is "about the way that tsunamis develop", and it modifies the word "explain". The correct abbreviation would be ADV, as it is an adverb phrase modifying the verb "explain".
6/ The prepositional phrase is "of an earthquake or volcanic activity", and it modifies the word "result". The correct abbreviation would be ADJ, as it is an adjective phrase modifying the noun "result".
7/ The prepositional phrase is "of Amber", and it modifies the word "formation". The correct abbreviation would be ADJ, as it is an adjective phrase modifying the noun "formation".
8/ The prepositional phrase is "of trees", and it modifies the word "resin". The correct abbreviation would be ADJ, as it is an adjective phrase modifying the noun "resin".
9/ The prepositional phrase is "along the timeline", and it modifies the word "displayed". The correct abbreviation would be ADV, as it is an adverb phrase modifying the verb "displayed".
10/ The prepositional phrase is "in thirty minutes", and it modifies the word "concludes". The correct abbreviation would be ADJ, as it is an adjective phrase modifying the noun "concludes".