Jane is in the meeting room.
"Is" in the sentence could be delusive, so I am going to replace "is" with another word.
Jane stays in the meeting room.
Then I make a gerund.
Staying in the meeting room.
This is a gerund, so that nobody cares who stays. In addition, you can simplify the phrase to:
Isn't it obvious that the "there" modifies "staying"? And remember I replaced "is" with "stay".
Jane, along with other students, is in the meeting room.
This is tough one. If the interpretation is "Jane who is along with other students is in the meeting", the phrase is adjective. However, due to the commas, it doesn't sound that way, but rather:
Being along with other students, Jane is in the meeting room.
And I am going to rephrase it to:
Jane is along with other students and in the meeting room.
To this sentence, you can apply the logic as described for the former sentence.
Honestly, I have a feeling that you could say there is a trick, because you can interpret these sentences different ways, which may lead to different conclusions. But, most prepositional phrases are adverbial unless they directly connect with nouns.