** you made errors in transcription. my answer below is based on correct transcription taken from https://www.beatthegmat.com/colonial-period-t114277.html

(A) After the Colonial period's 50 percent mortality rate, life expectancy improved for
children, but
first of all you need an event/time period after "after". secondly, 50% rate was in colonial period not a possession of colonial period implying mortality of colonial period. even if both of these were correct, (a) would be wrong because it is run-on

(B) Even though children's life expectancy, which improved over the Colonial period's 50
percent mortality rate,
errors similar to those mentioned above in (a) - even though needs a clause, and error in Colonial period's 50 percent mortality rate. post back if you don't see them.

(C) Although life expectancy for children improved after the Colonial period, during which
the mortality rate was 50 percent,
all correct

(D) While there was an improvement in life expectancy for children after the 50 percent
mortality rate of the Colonial period, still
life expectancy for children is incorrect. life expectancy of children is correct. 50 percent mortality rate of the Colonial period is incorrect. use of there is incorrect, it must refer to a place.

(E) Despite children's life expectancy improvement from the Colonial period's 50 percent
mortality rate,
Despite needs a clause