Each of the participants in the seminar on linguistics needs to regist

My answer is (B). It took me 01:35, most of which was spent deliberating between (B) and (D).

(A) "their" in "their textbooks" does not agree with "each".

(B) No obvious error. Keep for now.

(C) "their" in "their final payment" does not agree with "each".

(D) "his or her" does agree with "each". Keep for now.

(E) "have ordered" is not parallel with "register" and "send". The three verbs are supposed to be a list.
Note that "before April 12" and "no later than April 12" are not exactly the same. But the meaning change alone should not be ground to eliminate this option.

Now, back to (BD). After matching word for word to confirm that they only differ in "his or her" introduced in (D), I decide to choose (B) for two reasons:
(1) For perfect parallelism, (D) should add "his or her" before "final payment".
(2) Shorter is better. (B) is shorter than (D).

Eliminate D, and E - His or her is most of the time grammertically wrong, when refer to singular subject
D) send final payment no later than April 12, and order his or her textbooks at least two weeks before classes begin.
E) send final payment before April 12, and have ordered his or her textbooks at least two weeks before classes begin

Eliminate A, and C - Pronoun Error - Each of the participants: singular, their - plural
A) send final payment no later than April 12, and order their textbooks at least two weeks before classes begin.
C) send their final payment no later than April 12, and order textbooks at least two weeks before classes begin.

Correct Option B - verb list maintains parallelism
Each of the participants in the seminar on linguistics
- needs to register by March 1
- send final payment no later than April 12, and
- order textbooks at least two weeks before classes begin.