Re. cruising solo. Probably no one will even notice. We've been married for 19 years but we are not the joined at the hip type, so usually spend some time together, some apart, even for meals. You will find a lot of people like that, plus other solo cruisers.
And whether people like it or not, Carnival dress code, especially for a short 4 day cruise is very relaxed. There are other cruise lines that cater to those who want everybody to dress up, but NCL and Carnival both have adopted a more mainstream approach. Even for formal night, a dress shirt and tie or bolo is quite acceptable. As long as you look nice, you'll be fine.