Hi, you cover the alternatives well.
A basic rule is that a capital letter is used after a full stop, question and exclamation mark, and not after a comma, colon or semicolon. So b. "Dear Reader: this essay is about..." is correct, and also d is correct. However, don't go make the sentence too long.
In answer to question 2, the answer d sounds best to me.
d. "I am continuing my mission of sharing with you the information about..."
I would use the continuous form, because it is like "I am writing to you about". The noun "mission" allows both forms infinitive "to share" and gerund "sharing", but I feel that the second is better.