"REGARD AS" and "CONSIDER TO BE"

Many historians regard the time of the Heian court as the greatest period in Japanese history.
A. Same
B. regard the time of the Heian court to be
C. regard the time of the Heian court to have been
D. consider that the time of the Heian court is
E. consider the time of the Heian court as

The correct relevant idiomatic expression are "regard as" and "consider to be". Eliminate B, C and E. D is wrong tense. A is correct.

sentence with-
consider as   X
regard to be  X

conclusion that VS conclusion of

Henry never showed effort, and his essays were always pedestrian; since his latest paper is nearly flawless, the obvious conclusion seems to be one of a more advanced student researching and writing at least part of Henry's impressive essay.
A. Same
B. conclusion of a more advanced student researching and writing at least part of Henry's impressive essay seems obvious
C. conclusion seems obvious that at least part of Henry's impressive essay was researched and written by a more advanced student.
D. conclusion of at least part of Henry's impressive essay having been researched and written by a more advanced student seems obvious.
E. seemingly obvious conclusion is that a more advanced student would have researched and written at least part of Henry's impressive essay.

"Conclusion that" is correct.
"Conclusion of" is wrong. Therefore, A, B and D are out.
The tense is wrong in E. C is correct.

SO MUCH......AS

SO MUCH.......AS  is a very frequent idiom in the GMAT.

so much by X as by Y
so much because of X as because of Y

Q. Some analysts of the latest technological advances argue that technology moves forward not so much because of great sparks of ideas but because of smaller contributions, such as improved practices, better laboratories and more knowledgeable designers.
A. same
B. because of great sparks of ideas as the results of
C. because of great sparks of ideas as because of
D. through great sparks of ideas but through
E. through great sparks of ideas but results from

answer is C

Q. Ripe peaches are marked not so much by their color but instead by their firmness and fullness of aroma.
A. Same
B. rather than
C than
D. as
E. so much as

Correct Answer: D

JUST AS...SO TOO

JUST AS...SO TOO is idiomatically correct.

E.g. Just as the Russian communists of the early 20th century believed that they were overcoming the tyranny of the czars, so too did the Chinese communists believe they were avoiding the misrule of the Guomindang.

"LESS THAN" VS "LESSER THAN"

Q. With total sales of less than three hundred thousand dollars and fewer new subscribers than last year, the New England Theater Company is in danger of losing its building.

A. of less than three hundred thousand dollars and fewer

B. lower than three hundred thousand dollars and less

C. lesser than three hundred thousand dollars and fewer

D. fewer than three hundred thousand dollars and less

E. of fewer than three hundred thousand dollars and of fewer

For countable nouns we use "fewer".  So, it comes down to A, C and E. E uses "of fewer", which is not correct. "Lesser than" is idiomatically incorrect, "Less Than" is correct. Therefore, A is correct.

"FORBID FROM" "FORBID THAT"

"FORBID FROM" "FORBID THAT" both are idiomatically incorrect.

e.g.
No school policies forbid a teacher to scold a student. (correct)

FEWER THAN

FEWER THAN is correct idiom just as LESS THAN, GREATER THAN etc.

If the draft is not re-instated, less people will join the army in the coming 10 years than did in any other 10-year period in our nation's history.
A. Same
B. less people will be joining the army in the coming 10 years as
C. Fewer people will join the army in the coming 10 years as
D. Fewer people will be joining the army in the coming 10 years as
E. Fewer people will join the army in the coming 10 years than

"Fewer...as" is not the correct idiom when there is comparison, as is used for showing similarity so only option E is correct.