oh my gosh that's a lot of questions.
most of these are distinctions i've never consciously thought about, even though i've used a lot of them in my writing, so we can think of this as exploring together! (seriously)

akhpad wrote:

2.
so + adj/adv + that
such + adj + noun + that
Don is so tall that he can reach the top shelf without any effort.
Don is such a tall boy that he can reach the top shelf without any effort.=> is it correct?

i think your example here is fine, although it's unnecessary; if the emphasis is on a quality described by an adjective ("tall"in this example), then it's more compact and stylistically better to write "so + adj + that".
you are more likely to see the second of these constructions if the quality itself is embodied by a noun rather than by an adjective. for instance, Tom is such a hermit that he hasn't left his house in two years.
in that sentence, the quality is actually described by a noun ("hermit"), so there is no option to use the "so + adj + that" construction.

3.
The box is so heavy that I can’t lift it.
It is such a heavy box that I can’t lift it.
what is the difference in meaning.

exactly the same situation as #2. if you wrote the latter sentence as "it is such a monolith that i can't lift it", then, better.

4.
She worked hard and she made herself ill.
She worked so hard that she made herself ill.
She worked so hard as to make herself ill.
Is it correct? What is the change in meaning?

the first one -- the one with just "and" -- is incorrect unless you are actually implying that these are two separate, independent things. for instance, if this woman worked really hard and then drank alcohol until she began to vomit, the first sentence would make sense. if working hard is the cause of her illness, then the first sentence is incorrect.

the second and third constructions are a lot like each other; i don't think that gmac will ask you to distinguish between them. (if you see a split like that in a problem, then scour the choices for other differences.)
nevertheless, i think i can give you some sort of explanation: in general, you don't use so ADJ as to VERB unless the VERB describes some sort of state/condition. i.e., if the verb is an action verb, this construction generally isn't used.
for instance,
i am so ugly as to be viscerally repulsive to women. --> this works, because the verb "to be" describes a state/condition.
i am so ugly as to repel women on sight. --> you generally wouldn't see this in good writing, as "repel" is an action verb; the sentence would probably be written as i am so ugly that i repel women on sight.

rest assured that the above discussion is MUCH more subtle/writerly than anything that will actually be tested on this exam.

5.
"so as to" and "so + adj + as to"
I called him in order to invite him.
I called him to invite him.
I called him so as to invite him.
What is the change in meaning?

very interesting.
there's not really a difference in the first two. in general, "in order to" works better in longer sentences -- sentences in which there are so many words that "to" by itself would lead to a confusing/unreadable sentence.

"so as to" is an interesting construction. i don't think that gmac likes it very much -- i've never seen it in an officially correct answer -- but i think the main distinction is that it's used to describe indirect intentions.
for instance, the example above isn't great because you are calling this person directly to invite him, so you should use one of the earlier two versions.

on the other hand, consider the following: Joe bought a gym membership so as to become more attractive to women.
this is what i mean by indirect intention. obviously, the act of buying a gym membership itself is not going to make joe instantly more attractive to women (women do not swoon over a man's gym membership card). instead, there are plenty of implied intermediate steps between "by a gym membership" and "be more attractive"; the use of "so as to" implies that there are such intermediate steps in the process.

once again, this is a very writerly difference. i think it's fun to try to explicate it -- i've definitely never thought about these things consciously before -- but i can guarantee that you will not be tested on this kind of difference.

6.
I study so that I can get a good grade.
I study so as to get a good grade.

same distinction as above.
if you are talking about getting a good grade on the actual exam you are studying for, then this is a direct intention, and so the first sentence works better.
if you are talking about getting a good grade in the entire course, then this is an indirect intention, and so the second sentence is better.

once again, this kind of difference will never be tested on the gmat. however, if it ever helps you become a professional writer, then you can thank me.

I study so hard that I can get a good grade.
I study so hard as to get a good grade.

remember that "so + adj + that" indicates some sort of extreme quality. so, the first of these sentences probably doesn't make sense, unless getting a good grade is presented as some sort of extreme, unusual achievement.
for instance, let's say there's a class called "math X" at some university, and that this class is so difficult that only one in every thousand students even gets a passing grade.
in that case, "i study sooooo hard that i can actually get a good grade in math X" makes sense. on the other hand, if this is just a sentence about normal intentions, then it's wrong.

the second one doesn't make sense; see my notes about "so ____ as to ____" above.

Congress is debating a bill requiring certain employers to provide workers with unpaid leave so as to care for sick or newborn children. => INCORRECT

this is a whole different issue. in the construction "so as to", there is no change of subject, and so there's an implication that the subject is the same as the subject of the previous clause/action.

that's a big issue here, because the only subjects of actions in the previous clauses are "congress" and "certain employers". therefore, the sentence is implying that one of these two entities is actually going to care for sick or newborn children! not good.
the sentence needs to be written in a way that changes the subject.