The correct answer for Blank (i) is A. auspicious and for Blank (ii) is E. calumny.

Here is the breakdown of why this is the correct combination:
The word "Despite" sets up a contrast. The first part of the sentence describes a positive beginning to the campaign, which is then contrasted with the negative second part, which talks about it devolving into something bad.
- Blank (i): This blank needs a word that means a positive or promising beginning.
- A. auspicious: This means conducive to success; favorable. It perfectly describes a promising or good start to an election campaign.
- B. turbulent means characterized by conflict, disorder, or confusion, which is the opposite of the needed meaning.
- C. publicized means widely known or advertised, which is a neutral term and doesn't fit the positive context.
- Blank (ii): The blank needs a word that, along with "acrimony" and "casting aspersions," describes a negative and bitter turn in the campaign. "Casting aspersions" means to make a damaging or negative remark about someone.
- E. calumny: This means the making of false and defamatory statements about someone in order to damage their reputation; slander. This fits perfectly with "casting aspersions" and "acrimony."
- D. capitulation means the action of surrendering or ceasing to resist an opponent or demand. This doesn't fit the context of a fight or conflict.
- F. serenity means the state of being calm, peaceful, or untroubled, which is the opposite of the negative mood described.

Therefore, the completed sentence is: "Despite a(n) auspicious beginning, the election campaign quickly devolved into calumny and acrimony, with each side casting aspersions."