The new “e-waste” salvage

[RonPurewal]

* From context, it should be clear what "that" is modifying (= waste items).

* You need to re-calibrate your idea of "too far away" for this kind of modifier. Check out, e.g., #50 in the OG diagnostic chapter (not the regular sentence correction chapter).
"That" has much greater latitude to describe long phrases than "which" does.

* You put "too far away" in boldface.
Is there a special significance there? If so, I didn't catch it.

[RonPurewal]

"Who(se)" can do the same thing. E.g., you can have members of the gym whose contracts are due to expire in the next month.

Not sure why you have "where""”a completely different kind of thing"”grouped in there with "who" and "whose". Is that a typographical error?

[RonPurewal]

I love Manhattan in New York where I worked in 2012.

I don't know what 'where' modifies in the second sentence.

Manhattan or New York?

Here, you're getting into issues that the GMAT doesn't test"”namely, the presence/absence of commas in modifiers.

If you don't have a comma before "where", then you're qualifying the previous noun.
E.g.,

My wife would often visit me at the commissary, where I worked six days a week.
--> Here, "where I worked..." does not qualify/narrow down "commissary". I.e., either (a) there's only one commissary, or else (b) the sentence occurs in a context in which the particular commissary has already been specified.

My wife would often visit me at the commissary where I worked six days a week.
--> There's more than one commissary. I'm specifically referring to the one where I worked.

So, neither of your sentences really makes any sense, because there's only one Shanghai, only one Manhattan in New York, and only one New York. Both sentences are nonsense unless a comma precedes where.

If you put a comma into the Shanghai sentence, its meaning is clear.

If you put a comma into the second sentence, the only reasonable interpretation is that you worked in "Manhattan in New York".
If you actually want to express the idea that you love Manhattan but you worked elsewhere in the state, then obviously you would have to be explicit about that.

[RonPurewal]

Also, don't forget"”nothing in the above post has ever been tested by GMAC.