I see a lot of complicated explanations involving the use of grammatical terms. While most of these explanations are accurate , i believe that when we prioritize grammar over
the meaning, we may miss the sky for the stars. We have 3 verbs in the sentence. If we recognize the correct sequence of the actions, then the keys to the kingdom will be ours.

The 3 verbs in the sentence are

- Attend
- Receive
- Develop

a) We need to understand the importance and sequence of EACH OF these verbs. The actions which are parallel need to be in same tense.
b) "AND" is usually a parallelism marker. The word "AND" can either indicate a set of events that happen AT THE SAME TIME, or indicate a SEQUENCE of events that happen one after the other.
c) Remember for a list of 3 or more items that are described using the word "AND", GMAT always uses a ,comma to separate the last item.
E.g: red, blue ,and green.
E.g : John, jane, jacob ,and Chris

A detour :-
Let's look at a few examples. Full Disclosure : These examples are based on a couple of examples that i have seen Ron Purewal (MGMAT fame) use. Somehow, examples that require one to visualize someone else eating, burping and slurping turn out to be the ones that kinda burn concepts into our memory .

John ate the pizza, slurping loudly and burping regularly - IMPLIES THAT JOHN ATE THE PIZZA AND WHILE EATING, JOHN MADE SLURPING AND BURPING SOUNDS.
John ate the pizza, slurped loudly and ,burped regularly - IMPLIES THAT JOHN FINISHED EATING THE PIZZA FIRST AND THEN AFTER EATING , HE MADE SLURPING SOUNDS (second) AND AFTER HE MADE SLURPING SOUNDS, HE MADE BURPING SOUNDS(third).
John ate the pizza, slurping loudly and burped regularly- IMPLIES THAT JOHN ATE THE PIZZA AND WHILE EATING THE PIZZA, HE MADE SLURPING SOUNDS and AFTER HE FINISHED EATING(and slurping), he MADE BURPING SOUNDS.

Typically -
[*]A ,COMMA VERB-ing modifier (E.g : burping and slurping in the above examples) tends to describe the main verb in the preceding clause.
[*]A VERB - ING-modifier WITHOUT A COMMA is attached to the preceding noun.

A couple of Examples :-
[*]John watched Sam running around a tree. (Meaning - Sam was running around a tree and John saw him. Note the absence of a COMMA)
[*]John watched Sam,using a pair of binoculars.(Meaning - John used a pair of binoculars to watch Same)

Back to the question :-
MEANING OF THE GIVEN SENTENCE :
Albert Einstein attended some college and during his period of attendance, he received training and developed something. The main verb of the sentence is is "Attended" and the other terms "Receive" and "develop" are VERB-ing modifiers that describe the how Albert Einstein attended college.

CORRECT ANSWER :-
(A) attended the Swiss Federal Polytechnic School in Zurich, receiving in-depth training in quantitative analysis, and developing

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This is Superficial Parallelism. The Main verb is attended, So it need not be in sync with the other verbs. Receiving and Developing should be in parallel.
So Answer is : A

After moving to Switzerland in the 1890’s, Albert Einstein attended the Swiss Federal Polytechnic School in Zurich, receiving in-depth training in quantitative analysis and developing a foundation for his future work in mathematical physics.

A lot of the approaches for this question revolved about elimating the wrong answer choice-which is fine. What I didn't get was how a noun modifier could be so far away from the noun it modifies. It seems as if receiving is modifying school (or Zurich?) rather than Albert Einstein. To me that is incorrect

Could someone explain how we are to know that it modifies Albert Einstein grammatically?
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A is the right answer.

Attended is the main action. Receiving and Attending are a consequence of this main action. So, only these two need to be parallel. The Q. stem states the sentence correctly.

Option A: Einstein attended the ....in Zurich, (subordinate phrase starts) receiving A and developing B (subordinate phrase ends). This is correct usage.
Option B: Einstein attended the ....in Zurich, (subordinate phrase starts) receiving A and developed B (subordinate phrase ends). If there was a comma after "receiving A", then this statement would have been correct. Because then A would act as a subordinate phrase and B would be a continuation of the original sentence and should be in simple past.
Option C: The pronoun "he" is not needed.
Option D: "developing" is wrong. It should be "and developed".
Option E: This is entirely wrong. Continuous form should be complemented with simple past.