Prepgmat09, I will take a stab at explaining your doubt about comparison 2 in your post.
Sentence in Question:
Research shows that marrying and raising a family remains a key objective of most young Americans, like that of other cultures.
Comparison 2 per your post:
Noun Phrase 1: key objective of most young Americans
Noun Phrase 2: that of other cultures (here, "that" refers to "key objectives")
Translating this comparison and simplifying the sentence we can form the following sentence:
XYZ is a key objective of Americans, like that of other cultures.
OR
XYZ is a key objective of Americans, like objectives of other cultures.
Since the comparison word "like" is used here, we need to make sure that the comparison is logically and grammatically parallel.
Here XYZ (a specific objective) is being compared to objectives (general). Thus, this comparison is not parallel.
If you are not able to deduce this comparison from this sentence structure, then for ease of understanding, we will simply shuffle the phrase and clause in this sentence. Note that by doing the following shuffling, the sentence essentially remains the same.
Like objectives of other cultures, XYZ is an objective of Americans.
Now the entities being compared may be more clear:
Objectives (general) LIKE XYZ (a specific objective)
I hope this explains why the comparison#2 stated in your post is not correct comparison.
One more thing about the use of 'like' and 'as':
'Like' is used to establish "similarity in behavior" whereas 'as' is used to establish the 'actual function'.
For example, both these sentences are correct, but they communicate different meaning:
Joe acts as Susan's mentor = This implies that Joe is Susan's mentor.
Joe acts like Susan's mentor = This implies that Joe is not Susan's mentor but he behaves like one.
For e-GMAT users, these concepts are explained in detailed in the concept file:
Idioms - Functions - I.
Furthermore, the strategy of simplifying the sentence to understand the meaning is applied in all application files.
