Answer: C) subordinating conjunction.
Explanation: a subordinating conjunction is a word that joins a dependent or subordinate clause (a phrase that doesn't have complete meaning on its own) with an independent clause (it has complete meaning on its own). There are subordinating conjunctions that show a relationship between two clauses involving a transition of time or place. In this case, "after" is a subordinating conjunction joining the independent clause "Mrs. Jenkins thanked them gratefully" and the subordinate clause "After the police came to her rescue."
2 for the first and 3 for the second
'Finally' is the answer the others don't make sense if you try to read them with the rest of the sentence.
Assuming we're just looking at this phrase, "learn'd" suggests that the astronomer studied to become intelligent in the astronomical field.