B - which was approved April 24, 1800 is acting as a non restrictive relative clause here as it is enclosed within commas. So this is not central to the sentence. Removing that part, the sentence would look like - The act of Congress making provision...Washington DC, also established the Library of Congress.. Use of present participle making is incorrect here.

C - which made provision for...Washington DC is critical to the core meaning of the sentence and must be introduced by that and not which. Use of and is superfluous.

D - Misplaced modifiers, Incorrect use of present participle making.

E - made provision for the removal of the government of the US to the new federal city Washington DC has lost its modifier property because of lack of relative pronoun that.

A - Approved April 24, 1800 and that made provision ...Washington DC perfectly modify the act of congress. Use of also is best justified in this statement..

A is thus correct.

Approved April 24, 1800, the act of Congress that made provision for the removal of the government of the United States to the new federal city, Washington, D.C., also established the Library of Congress.

A. Approved April 24, 1800, the act of Congress that made provision for the removal of the government of the United States to the new federal city, Washington, D.C., also established
B. The act of Congress, which was approved April 24, 1800, making provision for the removal of the government of the United States to the new federal city, Washington, D.C., also established
C. The act of Congress approved April 24, 1800, which made provision for the removal of the government of the United States to the new federal city, Washington, D.C., and established
D. Approved April 24, 1800, making provision for the removal of the government of the United States to the new federal city, Washington, D.C., the act of Congress also established
E. Approved April 24, 1800, the act of Congress made provision for the removal of the government of the United States to the new federal city, Washington, D.C., also establishing

The concepts tested in this SC:

1. Opening modifier:

An opening modifier is one that is used at the beginning and modifies the noun immediately after comma.

Example:
Built in 1990, the building has been destroyed in 2000.

Tired by traveling, John went to new market to buy a cool drink.

==> Opening Modifier + Comma + NOUN/Pronoun/Noun phrase

NOTE: Modifier + Modifier + Comma + NOUN-------> This construction is NOT correct for two reasons:

1. First modifier seems to modify the second modifier, leading to mis reading.
2. The NOUN being modified is placed very remote from the first modifier.

--> This kills the option D. Besides, "The act of congress also established" is not correct because there should have another verb before the verb "established" in order to use "also".

2. Non-essential modifier:

Non-essential modifiers are set off by commas (,...,). These modifiers can be eliminated from the sentence without losing the grammatical accuracy of the main sentence.

Now, we can apply this concept to the options B and C.

B. The act of Congress, which was approved April 24, 1800, making provision for the removal of the government of the United States to the new federal city, Washington, D.C., also established

the skeleton of the sentence is as follows:

The act of Congress also established.

------> The word "also" indicates that there is another verb performed by "the act of Congress"

So, this is out.


C. The act of Congress approved April 24, 1800, which made provision for the removal of the government of the United States to the new federal city, Washington, D.C., and established

The skeleton:

The act of Congress approved April 24, 1800 and established.

"...and established" indicates that there is another verb performed by the Act, but that is not here.

So, this is out.


3. Parallelism:

Third concept that has been tested in this SC is parallelism.

Example:

I have done the work and helped them.---Parallel.
BUT.
I have done the work and helping them.---NOT parallel.

Now, come to the option E.

E. Approved April 24, 1800, the act of Congress made provision for the removal of the government of the United States to the new federal city, Washington, D.C., also establishing

---> "Made" and "establishing" are NOT parallel. So E is out.

Only option A does not have problem.

Answer is A.

HTH.